Sectors - GRE Quantitative Reasoning
Card 0 of 120
If the outer arc of 1/12th of a circular pie is 7π, what is the area of 1/4th of the pie?
If the outer arc of 1/12th of a circular pie is 7π, what is the area of 1/4th of the pie?
Our initial data tells us that (1/12)c = 7π or (1/12)πd = 7π. This simplifies to (1/12)d = 7 or d = 84. Furthermore, we know that r is 42. Given this, we can ascertain the area of a quarter of the whole pie by taking one fourth of the whole area or 0.25 * π * 422 = 0.25 * 1764 * π = 441π
Our initial data tells us that (1/12)c = 7π or (1/12)πd = 7π. This simplifies to (1/12)d = 7 or d = 84. Furthermore, we know that r is 42. Given this, we can ascertain the area of a quarter of the whole pie by taking one fourth of the whole area or 0.25 * π * 422 = 0.25 * 1764 * π = 441π
Compare your answer with the correct one above
If the outer arc of 1/12th of a circular pie is 7π, what is the area of 1/4th of the pie?
If the outer arc of 1/12th of a circular pie is 7π, what is the area of 1/4th of the pie?
Our initial data tells us that (1/12)c = 7π or (1/12)πd = 7π. This simplifies to (1/12)d = 7 or d = 84. Furthermore, we know that r is 42. Given this, we can ascertain the area of a quarter of the whole pie by taking one fourth of the whole area or 0.25 * π * 422 = 0.25 * 1764 * π = 441π
Our initial data tells us that (1/12)c = 7π or (1/12)πd = 7π. This simplifies to (1/12)d = 7 or d = 84. Furthermore, we know that r is 42. Given this, we can ascertain the area of a quarter of the whole pie by taking one fourth of the whole area or 0.25 * π * 422 = 0.25 * 1764 * π = 441π
Compare your answer with the correct one above
If the outer arc of 1/12th of a circular pie is 7π, what is the area of 1/4th of the pie?
If the outer arc of 1/12th of a circular pie is 7π, what is the area of 1/4th of the pie?
Our initial data tells us that (1/12)c = 7π or (1/12)πd = 7π. This simplifies to (1/12)d = 7 or d = 84. Furthermore, we know that r is 42. Given this, we can ascertain the area of a quarter of the whole pie by taking one fourth of the whole area or 0.25 * π * 422 = 0.25 * 1764 * π = 441π
Our initial data tells us that (1/12)c = 7π or (1/12)πd = 7π. This simplifies to (1/12)d = 7 or d = 84. Furthermore, we know that r is 42. Given this, we can ascertain the area of a quarter of the whole pie by taking one fourth of the whole area or 0.25 * π * 422 = 0.25 * 1764 * π = 441π
Compare your answer with the correct one above
An ant begins at the center of a pie with a 12" radius. Walking out to the edge of pie, it then proceeds along the outer edge for a certain distance. At a certain point, it turns back toward the center of the pie and returns to the center point. Its whole trek was 55.3 inches. What is the approximate size of the angle through which it traveled?
An ant begins at the center of a pie with a 12" radius. Walking out to the edge of pie, it then proceeds along the outer edge for a certain distance. At a certain point, it turns back toward the center of the pie and returns to the center point. Its whole trek was 55.3 inches. What is the approximate size of the angle through which it traveled?
To solve this, we must ascertain the following:
-
The arc length through which the ant traveled.
-
The percentage of the total circumference in light of that arc length.
-
The percentage of 360° proportionate to that arc percentage.
To begin, let's note that the ant travelled 12 + 12 + x inches, where x is the outer arc distance. (It traveled the radius twice, remember); therefore, we know that 24 + x = 55.3 or x = 31.3.
Now, the total circumference of the circle is 2πr or 24π. The arc is 31.3/24π percent of the total circumference; therefore, the percentage of the angle is 360 * 31.3/24π. Since the answers are approximations, use 3.14 for π. This would be 149.52°.
To solve this, we must ascertain the following:
-
The arc length through which the ant traveled.
-
The percentage of the total circumference in light of that arc length.
-
The percentage of 360° proportionate to that arc percentage.
To begin, let's note that the ant travelled 12 + 12 + x inches, where x is the outer arc distance. (It traveled the radius twice, remember); therefore, we know that 24 + x = 55.3 or x = 31.3.
Now, the total circumference of the circle is 2πr or 24π. The arc is 31.3/24π percent of the total circumference; therefore, the percentage of the angle is 360 * 31.3/24π. Since the answers are approximations, use 3.14 for π. This would be 149.52°.
Compare your answer with the correct one above
A study was conducted to determine the effectiveness of a vaccine for the common cold (Rhinovirus sp.). 1000 patients were studied. Of those, 500 received the vaccine and 500 did not. The patients were then exposed to the Rhinovirus and the results were tabulated.
Table 1 shows the number of vaccinated and unvaccinated patients in each age group who caught the cold.
Suppose the scientists wish to create a pie chart reflecting a patient's odds of catching the virus depending on vaccination status and age group.
All 1000 patients are included in this pie chart.
What would be the angle of the arc for the portion of the chart representing vaccinated patients of all age groups who caught the virus?
A study was conducted to determine the effectiveness of a vaccine for the common cold (Rhinovirus sp.). 1000 patients were studied. Of those, 500 received the vaccine and 500 did not. The patients were then exposed to the Rhinovirus and the results were tabulated.
Table 1 shows the number of vaccinated and unvaccinated patients in each age group who caught the cold.
Suppose the scientists wish to create a pie chart reflecting a patient's odds of catching the virus depending on vaccination status and age group.
All 1000 patients are included in this pie chart.
What would be the angle of the arc for the portion of the chart representing vaccinated patients of all age groups who caught the virus?
First, we must determine what proportion of the 1000 patients were vaccinated and caught the virus. The total number of patients who were vaccinated and caught the virus is 50.
18 + 4 + 5 + 4 + 19 = 50
The proportion of the patients is represented by dividing this group by the total number of participants in the study.
50/1000 = 0.05
Next, we need to figure out how that proportion translates into a proportion of a pie chart. There are 360° in a pie chart. Multiply 360° by our proportion to reach the solution.
360° * 0.05 = 18°
The angle of the arc representing vaccinated patients who caught the virus is 18°.
First, we must determine what proportion of the 1000 patients were vaccinated and caught the virus. The total number of patients who were vaccinated and caught the virus is 50.
18 + 4 + 5 + 4 + 19 = 50
The proportion of the patients is represented by dividing this group by the total number of participants in the study.
50/1000 = 0.05
Next, we need to figure out how that proportion translates into a proportion of a pie chart. There are 360° in a pie chart. Multiply 360° by our proportion to reach the solution.
360° * 0.05 = 18°
The angle of the arc representing vaccinated patients who caught the virus is 18°.
Compare your answer with the correct one above
A group of students ate an 
-inch pizza that was cut into 
equal slices. What was the angle measure needed to cut this pizza into these equal slices?
A group of students ate an
You will not need all of the information given in the prompt in order to answer this question successfully. You really only need to know that there were 
slices. If the slices were evenly divided among the 
degrees of the pizza, this means that the degree measure of each slice was 
. This reduces to 
degrees.
You will not need all of the information given in the prompt in order to answer this question successfully. You really only need to know that there were
Compare your answer with the correct one above
An ant begins at the center of a pie with a 12" radius. Walking out to the edge of pie, it then proceeds along the outer edge for a certain distance. At a certain point, it turns back toward the center of the pie and returns to the center point. Its whole trek was 55.3 inches. What is the approximate size of the angle through which it traveled?
An ant begins at the center of a pie with a 12" radius. Walking out to the edge of pie, it then proceeds along the outer edge for a certain distance. At a certain point, it turns back toward the center of the pie and returns to the center point. Its whole trek was 55.3 inches. What is the approximate size of the angle through which it traveled?
To solve this, we must ascertain the following:
-
The arc length through which the ant traveled.
-
The percentage of the total circumference in light of that arc length.
-
The percentage of 360° proportionate to that arc percentage.
To begin, let's note that the ant travelled 12 + 12 + x inches, where x is the outer arc distance. (It traveled the radius twice, remember); therefore, we know that 24 + x = 55.3 or x = 31.3.
Now, the total circumference of the circle is 2πr or 24π. The arc is 31.3/24π percent of the total circumference; therefore, the percentage of the angle is 360 * 31.3/24π. Since the answers are approximations, use 3.14 for π. This would be 149.52°.
To solve this, we must ascertain the following:
-
The arc length through which the ant traveled.
-
The percentage of the total circumference in light of that arc length.
-
The percentage of 360° proportionate to that arc percentage.
To begin, let's note that the ant travelled 12 + 12 + x inches, where x is the outer arc distance. (It traveled the radius twice, remember); therefore, we know that 24 + x = 55.3 or x = 31.3.
Now, the total circumference of the circle is 2πr or 24π. The arc is 31.3/24π percent of the total circumference; therefore, the percentage of the angle is 360 * 31.3/24π. Since the answers are approximations, use 3.14 for π. This would be 149.52°.
Compare your answer with the correct one above
A study was conducted to determine the effectiveness of a vaccine for the common cold (Rhinovirus sp.). 1000 patients were studied. Of those, 500 received the vaccine and 500 did not. The patients were then exposed to the Rhinovirus and the results were tabulated.
Table 1 shows the number of vaccinated and unvaccinated patients in each age group who caught the cold.
Suppose the scientists wish to create a pie chart reflecting a patient's odds of catching the virus depending on vaccination status and age group.
All 1000 patients are included in this pie chart.
What would be the angle of the arc for the portion of the chart representing vaccinated patients of all age groups who caught the virus?
A study was conducted to determine the effectiveness of a vaccine for the common cold (Rhinovirus sp.). 1000 patients were studied. Of those, 500 received the vaccine and 500 did not. The patients were then exposed to the Rhinovirus and the results were tabulated.
Table 1 shows the number of vaccinated and unvaccinated patients in each age group who caught the cold.
Suppose the scientists wish to create a pie chart reflecting a patient's odds of catching the virus depending on vaccination status and age group.
All 1000 patients are included in this pie chart.
What would be the angle of the arc for the portion of the chart representing vaccinated patients of all age groups who caught the virus?
First, we must determine what proportion of the 1000 patients were vaccinated and caught the virus. The total number of patients who were vaccinated and caught the virus is 50.
18 + 4 + 5 + 4 + 19 = 50
The proportion of the patients is represented by dividing this group by the total number of participants in the study.
50/1000 = 0.05
Next, we need to figure out how that proportion translates into a proportion of a pie chart. There are 360° in a pie chart. Multiply 360° by our proportion to reach the solution.
360° * 0.05 = 18°
The angle of the arc representing vaccinated patients who caught the virus is 18°.
First, we must determine what proportion of the 1000 patients were vaccinated and caught the virus. The total number of patients who were vaccinated and caught the virus is 50.
18 + 4 + 5 + 4 + 19 = 50
The proportion of the patients is represented by dividing this group by the total number of participants in the study.
50/1000 = 0.05
Next, we need to figure out how that proportion translates into a proportion of a pie chart. There are 360° in a pie chart. Multiply 360° by our proportion to reach the solution.
360° * 0.05 = 18°
The angle of the arc representing vaccinated patients who caught the virus is 18°.
Compare your answer with the correct one above
A group of students ate an -inch pizza that was cut into equal slices. What was the angle measure needed to cut this pizza into these equal slices?
A group of students ate an
You will not need all of the information given in the prompt in order to answer this question successfully. You really only need to know that there were slices. If the slices were evenly divided among the degrees of the pizza, this means that the degree measure of each slice was . This reduces to degrees.
You will not need all of the information given in the prompt in order to answer this question successfully. You really only need to know that there were
Compare your answer with the correct one above
An ant begins at the center of a pie with a 12" radius. Walking out to the edge of pie, it then proceeds along the outer edge for a certain distance. At a certain point, it turns back toward the center of the pie and returns to the center point. Its whole trek was 55.3 inches. What is the approximate size of the angle through which it traveled?
An ant begins at the center of a pie with a 12" radius. Walking out to the edge of pie, it then proceeds along the outer edge for a certain distance. At a certain point, it turns back toward the center of the pie and returns to the center point. Its whole trek was 55.3 inches. What is the approximate size of the angle through which it traveled?
To solve this, we must ascertain the following:
-
The arc length through which the ant traveled.
-
The percentage of the total circumference in light of that arc length.
-
The percentage of 360° proportionate to that arc percentage.
To begin, let's note that the ant travelled 12 + 12 + x inches, where x is the outer arc distance. (It traveled the radius twice, remember); therefore, we know that 24 + x = 55.3 or x = 31.3.
Now, the total circumference of the circle is 2πr or 24π. The arc is 31.3/24π percent of the total circumference; therefore, the percentage of the angle is 360 * 31.3/24π. Since the answers are approximations, use 3.14 for π. This would be 149.52°.
To solve this, we must ascertain the following:
-
The arc length through which the ant traveled.
-
The percentage of the total circumference in light of that arc length.
-
The percentage of 360° proportionate to that arc percentage.
To begin, let's note that the ant travelled 12 + 12 + x inches, where x is the outer arc distance. (It traveled the radius twice, remember); therefore, we know that 24 + x = 55.3 or x = 31.3.
Now, the total circumference of the circle is 2πr or 24π. The arc is 31.3/24π percent of the total circumference; therefore, the percentage of the angle is 360 * 31.3/24π. Since the answers are approximations, use 3.14 for π. This would be 149.52°.
Compare your answer with the correct one above
A study was conducted to determine the effectiveness of a vaccine for the common cold (Rhinovirus sp.). 1000 patients were studied. Of those, 500 received the vaccine and 500 did not. The patients were then exposed to the Rhinovirus and the results were tabulated.
Table 1 shows the number of vaccinated and unvaccinated patients in each age group who caught the cold.
Suppose the scientists wish to create a pie chart reflecting a patient's odds of catching the virus depending on vaccination status and age group.
All 1000 patients are included in this pie chart.
What would be the angle of the arc for the portion of the chart representing vaccinated patients of all age groups who caught the virus?
A study was conducted to determine the effectiveness of a vaccine for the common cold (Rhinovirus sp.). 1000 patients were studied. Of those, 500 received the vaccine and 500 did not. The patients were then exposed to the Rhinovirus and the results were tabulated.
Table 1 shows the number of vaccinated and unvaccinated patients in each age group who caught the cold.
Suppose the scientists wish to create a pie chart reflecting a patient's odds of catching the virus depending on vaccination status and age group.
All 1000 patients are included in this pie chart.
What would be the angle of the arc for the portion of the chart representing vaccinated patients of all age groups who caught the virus?
First, we must determine what proportion of the 1000 patients were vaccinated and caught the virus. The total number of patients who were vaccinated and caught the virus is 50.
18 + 4 + 5 + 4 + 19 = 50
The proportion of the patients is represented by dividing this group by the total number of participants in the study.
50/1000 = 0.05
Next, we need to figure out how that proportion translates into a proportion of a pie chart. There are 360° in a pie chart. Multiply 360° by our proportion to reach the solution.
360° * 0.05 = 18°
The angle of the arc representing vaccinated patients who caught the virus is 18°.
First, we must determine what proportion of the 1000 patients were vaccinated and caught the virus. The total number of patients who were vaccinated and caught the virus is 50.
18 + 4 + 5 + 4 + 19 = 50
The proportion of the patients is represented by dividing this group by the total number of participants in the study.
50/1000 = 0.05
Next, we need to figure out how that proportion translates into a proportion of a pie chart. There are 360° in a pie chart. Multiply 360° by our proportion to reach the solution.
360° * 0.05 = 18°
The angle of the arc representing vaccinated patients who caught the virus is 18°.
Compare your answer with the correct one above
A group of students ate an -inch pizza that was cut into equal slices. What was the angle measure needed to cut this pizza into these equal slices?
A group of students ate an
You will not need all of the information given in the prompt in order to answer this question successfully. You really only need to know that there were slices. If the slices were evenly divided among the degrees of the pizza, this means that the degree measure of each slice was . This reduces to degrees.
You will not need all of the information given in the prompt in order to answer this question successfully. You really only need to know that there were
Compare your answer with the correct one above
John owns 8 black shirts, 7 red shirts, 6 blue shirts and 4 white shirts. If he wants to make a circle chart of his shirts, what is the degree angle corresponding to the "blue shirt section?"
John owns 8 black shirts, 7 red shirts, 6 blue shirts and 4 white shirts. If he wants to make a circle chart of his shirts, what is the degree angle corresponding to the "blue shirt section?"
We can set up a ratio to calculate the angle measure as such: 6/25 = x/360, since there are 360 degrees in a circle. Solving, we obtain x = 86.4 degrees.
We can set up a ratio to calculate the angle measure as such: 6/25 = x/360, since there are 360 degrees in a circle. Solving, we obtain x = 86.4 degrees.
Compare your answer with the correct one above
A circular pie is cut into 30 pieces. Two people wish to split a piece of the pie, but one person wants to have twice as much as the other person. What is the angle of the smaller piece produced in this manner?
A circular pie is cut into 30 pieces. Two people wish to split a piece of the pie, but one person wants to have twice as much as the other person. What is the angle of the smaller piece produced in this manner?
First of all, calculate the angle of each of the full pieces of pie. This is easily found:
Though small, this is what the information tells us! Now, we know that if two people are eating the piece, with one having twice the amount of the other, the angles must be 
for the smaller piece and 
for the larger one. Thus, we can write the equation:
Simplifying, we get:
That is a tiny piece, but that is what is called for by the data!
First of all, calculate the angle of each of the full pieces of pie. This is easily found:
Though small, this is what the information tells us! Now, we know that if two people are eating the piece, with one having twice the amount of the other, the angles must be
Simplifying, we get:
That is a tiny piece, but that is what is called for by the data!
Compare your answer with the correct one above
Quantity A: The angle of a circle's sector having an arc length of 
and a radius of 
.
Quantity B: The angle of a circle's sector having an area of 
and a radius of 
.
Which of the following relations is true?
Quantity A: The angle of a circle's sector having an arc length of
Quantity B: The angle of a circle's sector having an area of
Which of the following relations is true?
For each of these, you need to compute the total measurement applicable to the given data. For Quantity A, this will be the total circumference. For Quantity B, this will be the total area. You will then divide the given sector calculation by this total amount. By multiplying this percentage by 
, you will find the degree measure of each; however, you will merely need to stop at the percentage (since both are percentages of the same number, namely 
).
Quantity A
The total circumference is calculated using the standard equation:
or, for our data: 
Thus, our pertinent percentage is:
Quantity B
For this, the area is computed by the formula:
or, for our data: 
Thus, our percentage is:
Clearly, 
, so A is larger than B.
For each of these, you need to compute the total measurement applicable to the given data. For Quantity A, this will be the total circumference. For Quantity B, this will be the total area. You will then divide the given sector calculation by this total amount. By multiplying this percentage by
Quantity A
The total circumference is calculated using the standard equation:
Thus, our pertinent percentage is:
Quantity B
For this, the area is computed by the formula:
Thus, our percentage is:
Clearly,
Compare your answer with the correct one above
John owns 8 black shirts, 7 red shirts, 6 blue shirts and 4 white shirts. If he wants to make a circle chart of his shirts, what is the degree angle corresponding to the "blue shirt section?"
John owns 8 black shirts, 7 red shirts, 6 blue shirts and 4 white shirts. If he wants to make a circle chart of his shirts, what is the degree angle corresponding to the "blue shirt section?"
We can set up a ratio to calculate the angle measure as such: 6/25 = x/360, since there are 360 degrees in a circle. Solving, we obtain x = 86.4 degrees.
We can set up a ratio to calculate the angle measure as such: 6/25 = x/360, since there are 360 degrees in a circle. Solving, we obtain x = 86.4 degrees.
Compare your answer with the correct one above
A circular pie is cut into 30 pieces. Two people wish to split a piece of the pie, but one person wants to have twice as much as the other person. What is the angle of the smaller piece produced in this manner?
A circular pie is cut into 30 pieces. Two people wish to split a piece of the pie, but one person wants to have twice as much as the other person. What is the angle of the smaller piece produced in this manner?
First of all, calculate the angle of each of the full pieces of pie. This is easily found:
Though small, this is what the information tells us! Now, we know that if two people are eating the piece, with one having twice the amount of the other, the angles must be for the smaller piece and for the larger one. Thus, we can write the equation:
Simplifying, we get:
That is a tiny piece, but that is what is called for by the data!
First of all, calculate the angle of each of the full pieces of pie. This is easily found:
Though small, this is what the information tells us! Now, we know that if two people are eating the piece, with one having twice the amount of the other, the angles must be
Simplifying, we get:
That is a tiny piece, but that is what is called for by the data!
Compare your answer with the correct one above
Quantity A: The angle of a circle's sector having an arc length of and a radius of .
Quantity B: The angle of a circle's sector having an area of and a radius of .
Which of the following relations is true?
Quantity A: The angle of a circle's sector having an arc length of
Quantity B: The angle of a circle's sector having an area of
Which of the following relations is true?
For each of these, you need to compute the total measurement applicable to the given data. For Quantity A, this will be the total circumference. For Quantity B, this will be the total area. You will then divide the given sector calculation by this total amount. By multiplying this percentage by , you will find the degree measure of each; however, you will merely need to stop at the percentage (since both are percentages of the same number, namely ).
Quantity A
The total circumference is calculated using the standard equation:
or, for our data:
Thus, our pertinent percentage is:
Quantity B
For this, the area is computed by the formula:
or, for our data:
Thus, our percentage is:
Clearly, , so A is larger than B.
For each of these, you need to compute the total measurement applicable to the given data. For Quantity A, this will be the total circumference. For Quantity B, this will be the total area. You will then divide the given sector calculation by this total amount. By multiplying this percentage by
Quantity A
The total circumference is calculated using the standard equation:
Thus, our pertinent percentage is:
Quantity B
For this, the area is computed by the formula:
Thus, our percentage is:
Clearly,
Compare your answer with the correct one above
John owns 8 black shirts, 7 red shirts, 6 blue shirts and 4 white shirts. If he wants to make a circle chart of his shirts, what is the degree angle corresponding to the "blue shirt section?"
John owns 8 black shirts, 7 red shirts, 6 blue shirts and 4 white shirts. If he wants to make a circle chart of his shirts, what is the degree angle corresponding to the "blue shirt section?"
We can set up a ratio to calculate the angle measure as such: 6/25 = x/360, since there are 360 degrees in a circle. Solving, we obtain x = 86.4 degrees.
We can set up a ratio to calculate the angle measure as such: 6/25 = x/360, since there are 360 degrees in a circle. Solving, we obtain x = 86.4 degrees.
Compare your answer with the correct one above
A circular pie is cut into 30 pieces. Two people wish to split a piece of the pie, but one person wants to have twice as much as the other person. What is the angle of the smaller piece produced in this manner?
A circular pie is cut into 30 pieces. Two people wish to split a piece of the pie, but one person wants to have twice as much as the other person. What is the angle of the smaller piece produced in this manner?
First of all, calculate the angle of each of the full pieces of pie. This is easily found:
Though small, this is what the information tells us! Now, we know that if two people are eating the piece, with one having twice the amount of the other, the angles must be for the smaller piece and for the larger one. Thus, we can write the equation:
Simplifying, we get:
That is a tiny piece, but that is what is called for by the data!
First of all, calculate the angle of each of the full pieces of pie. This is easily found:
Though small, this is what the information tells us! Now, we know that if two people are eating the piece, with one having twice the amount of the other, the angles must be
Simplifying, we get:
That is a tiny piece, but that is what is called for by the data!
Compare your answer with the correct one above