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Basic Geometry : Circles

Study concepts, example questions & explanations for Basic Geometry

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Example Questions

Example Question #141 : Circles

If the diameter of the circle is , what is the area of the shaded region?

Possible Answers:

14.63

12.05

15.82

13.90

Correct answer:

14.63

Explanation:

From the given figure, you should notice that the base of the triangle is the same as the diameter of the circle.

In order to find the area of the shaded region, we will first need to find the area of the circle and the area of the triangle.

Recall how to find the area of a circle:

$\text{Area of Circle}=\pi\times\text{radius}^2$

Now recall the relationship between the radius and the diameter.

$\text{Radius}=\frac{\text{Diameter}}{2}$

Plug in the value of the diameter to find the value of the radius.

$\text{Radius}=\frac{5}{2}$

Now, plug in the value of the radius in to find the area of the circle.

$\text{Area of Circle}=\pi\times (\frac{5}{2})^2=\frac{25}{4}\pi$

Next, recall how to find the area of a triangle.

$\text{Area of Triangle}=\frac{\text{base}\times\text{height}}{2}$

The height is already given by the question, and remember that the base is the same as the diameter of the circle.

Plug in these values to find the area of the triangle.

$\text{Area of Triangle}=\frac{5 \times 2}{2}=5$

We are now ready to find the area of the shaded region.

$\text{Area of Shaded Region}=\text{Area of Circle}-\text{Area of Triangle}$

$\text{Area of Shaded Region}=\frac{25}{4}\pi-5=14.63$

Remember to round to decimal places.

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Example Question #141 : How To Find The Area Of A Circle

If the diameter of the circle is , what is the area of the shaded region?

Possible Answers:

461.28

374.93

496.33

497.30

Correct answer:

374.93

Explanation:

From the given figure, you should notice that the base of the triangle is the same as the diameter of the circle.

In order to find the area of the shaded region, we will first need to find the area of the circle and the area of the triangle.

Recall how to find the area of a circle:

$\text{Area of Circle}=\pi\times\text{radius}^2$

Now recall the relationship between the radius and the diameter.

$\text{Radius}=\frac{\text{Diameter}}{2}$

Plug in the value of the diameter to find the value of the radius.

$\text{Radius}=\frac{26}{2}=13$

Now, plug in the value of the radius in to find the area of the circle.

$\text{Area of Circle}=\pi\times 13^2=169\pi$

Next, recall how to find the area of a triangle.

$\text{Area of Triangle}=\frac{\text{base}\times\text{height}}{2}$

The height is already given by the question, and remember that the base is the same as the diameter of the circle.

Plug in these values to find the area of the triangle.

$\text{Area of Triangle}=\frac{26 \times 12}{2}=156$

We are now ready to find the area of the shaded region.

$\text{Area of Shaded Region}=\text{Area of Circle}-\text{Area of Triangle}$

$\text{Area of Shaded Region}=169\pi-156=374.93$

Remember to round to decimal places.

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Example Question #143 : How To Find The Area Of A Circle

If the diameter of the circle is , what is the area of the shaded region?

Possible Answers:

289.37

291.57

292.66

116.71

Correct answer:

116.71

Explanation:

From the given figure, you should notice that the base of the triangle is the same as the diameter of the circle.

In order to find the area of the shaded region, we will first need to find the area of the circle and the area of the triangle.

Recall how to find the area of a circle:

$\text{Area of Circle}=\pi\times\text{radius}^2$

Now recall the relationship between the radius and the diameter.

$\text{Radius}=\frac{\text{Diameter}}{2}$

Plug in the value of the diameter to find the value of the radius.

$\text{Radius}=\frac{15}{2}$

Now, plug in the value of the radius in to find the area of the circle.

$\text{Area of Circle}=\pi\times \frac{15}{2}^2=\frac{225}{4}\pi$

Next, recall how to find the area of a triangle.

$\text{Area of Triangle}=\frac{\text{base}\times\text{height}}{2}$

The height is already given by the question, and remember that the base is the same as the diameter of the circle.

Plug in these values to find the area of the triangle.

$\text{Area of Triangle}=\frac{15 \times 8}{2}=60$

We are now ready to find the area of the shaded region.

$\text{Area of Shaded Region}=\text{Area of Circle}-\text{Area of Triangle}$

$\text{Area of Shaded Region}=\frac{225}{4}\pi-60=116.71$

Remember to round to decimal places.

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Example Question #141 : Radius

A circle has a radius of 3.5 cm . What is the area of the circle?

Possible Answers:

$3.5\pi cm ^2$

$7\pi cm^2$

$14\pi cm^2$

$12.25\pi cm^2$

$49\pi cm^2$

Correct answer:

$12.25\pi cm^2$

Explanation:

The formula for the area of a circle is:

$A=\pi r^2$

The radius of the circle is 3.5 cm , so we plug it into the formula, as follows:

$A=\pi (3.5)^2$

$A=12.25 \pi$

So the area of the circle is $12.25\pi cm ^2$ .

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Example Question #145 : How To Find The Area Of A Circle

The circumference of a circle is $19\pi cm$ . What is the area of the circle?

Possible Answers:

$90.25\pi cm^2$

$283.39\pi cm^2$

$19\pi cm^2$

There is not enough information given.

$361\pi cm^2$

Correct answer:

$90.25\pi cm^2$

Explanation:

The formula for the area of a circle is:

$A=\pi r^2$

In order to find this circle's area, we need to find it's radius, . We are not given the radius, but we are given the circumference, which can be used to find the radius.

The formula for the circumference of a circle is:

$C=2\pi r$

Because we know the circumference is $19\pi$ , we can plug that in for , as follows:

$19\pi=2\pi r$

We then solve for , as follows:

$\frac{19\pi}{\pi}=\frac{2\pi r}{\pi}$

19=2r

$\frac{19}{2}=r$

r=9.5

We now know the radius is 9.5 , so we plug this into the equation for area:

$A=\pi r^2$

$A= \pi(9.5)^2$

$A=90.25\pi$

Therefore, the area of the circle is $90.25\pi cm^2$ .

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Example Question #141 : Plane Geometry

If this circle has a diameter of 12 inches, what is its area?

Circle_12d

Possible Answers:

None of the other answers are correct.

$36\pi\ \text{inches}^{2}$

$26\pi\ \text{inches}^{2}$

$116\ \text{inches}^{2}$

$48\pi\ \text{inches}^{2}$

Correct answer:

$36\pi\ \text{inches}^{2}$

Explanation:

To find the area, we need to determine the radius of the circle first.

The radius is calculated as $r=\frac{D}{2}$ , where D is the diameter.

Given that the diameter is 12 inches, the radius is $r=\frac{12}{2}$ , or $r=6\ \text{inches}$ .

Next, we know that the formula for the area of the circle is $A=\pi r^2$ .

Using the radius we just found, we can find the area:

$A=\pi (6)^2=36\pi\ \text{inches}$

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Example Question #142 : How To Find The Area Of A Circle

Michael broke his clock, so he decides to make a new one. He wants the new clock to have a diameter of 16 inches. What will be the area of the new clock?

Possible Answers:

$64\pi^2$ inches

$256\pi^2$ inches

$62\pi^2$ inches

None of the answers given are correct.

$64\pi$ inches

Correct answer:

$64\pi^2$ inches

Explanation:

If the diameter is 16 inches, the radius is 8 inches. Now, just plug the radius into the equation to find the area of a circle.

$\pi r^2 = area$

$\pi 8^2 = area$

$\pi 64=area$

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Example Question #142 : Plane Geometry

A large pizza at Hogie's Pizza and Subs has a diameter of {20}'' and is cut into equal-sized slices. If slices of pizza are eaten by a group of friends, what is the area of the remaining pie? Round to the nearest tenth of an inch.

Possible Answers:

$314.2\;in^2$

$194.2\;in^2$

$183.3\;in^2$

$130.9\;in^2$

$125.7\;in^2$

Correct answer:

$130.9\;in^2$

Explanation:

Since of slices of pizza were eaten, the area of the remaining pie can be calculated as such:

$\\area=\frac{12-7}{12}\cdot\pi\cdot(10\;in)^2\\area=\frac{5}{12}\cdot3.14159\cdot100\;in^2$

$area=\frac{5}{12}\cdot314.159\;in^2\approx130.9\;in^2$

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Example Question #142 : Plane Geometry

If an {18}'' diameter frozen pizza is cut into equal sized slices, what would be the area of one slice of pizza?

Possible Answers:

$35.6\;in^2$

$31.8\;in^2$

$21.7\;in^2$

$29.8\;in^2$

$33.7\;in^2$

Correct answer:

$31.8\;in^2$

Explanation:

One slice of pizza represents $\frac{1}{8}$ the total area of the pizza. We can solve for the area using this formula:

$area=\frac{1}{8}\cdot\pi\cdot r^2$

$\\area=\frac{1}{8}\cdot3.14159\cdot(8\;in)^2\\area=\frac{1}{8}\cdot254.47\;in^2\approx31.8\;in^2$

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Example Question #144 : Radius

If the circumference of a circle is $30 \pi cm$ , what is the area?

Possible Answers:

$15 \pi cm^2$

$225 \pi cm^ 2$

$30 \pi cm^2$

$900 \pi cm^2$

Correct answer:

$225 \pi cm^ 2$

Explanation:

The circumference is found by using the formula $C = 2 \pi r$ where r is the radius. To find the radius, plug in the value for C:

$30 \pi = 2 \pi r$ divide both sides by 2 pi

15 = r

Now to find the area we can plug this radius into the formula $A = \pi r^2$ .

$A = \pi \cdot (15)^2 = 225 \pi$

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Basic Geometry : Circles

Study concepts, example questions & explanations for Basic Geometry

All Basic Geometry Resources

Example Questions

Example Question #141 : Circles

Example Question #141 : How To Find The Area Of A Circle

Example Question #143 : How To Find The Area Of A Circle

Example Question #141 : Radius

Example Question #145 : How To Find The Area Of A Circle

Example Question #141 : Plane Geometry

Example Question #142 : How To Find The Area Of A Circle

Example Question #142 : Plane Geometry

Example Question #142 : Plane Geometry

Example Question #144 : Radius

All Basic Geometry Resources

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