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GED Math : Geometry and Graphs

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4 Diagnostic Tests 263 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #81 : Geometry And Graphs

Find the circumference of a circle if the radius is $5\pi$ .

Possible Answers:

$10+2\pi$

$10+2\pi ^2$

$10\pi$

$10\pi^2$

$12\pi$

Correct answer:

$10\pi^2$

Explanation:

Write the formula for the circumference of a circle.

$A = 2\pi r$

Substitute the radius.

$A = 2\pi (5\pi) = 10\pi^2$

The answer is: $10\pi^2$

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Example Question #81 : Geometry And Graphs

Find the circumference of the circle with a diameter of $2\pi -3$ .

Possible Answers:

$4\pi ^2-6\pi$

$4\pi ^2-6$

$2\pi ^2-3\pi$

$4\pi^2-12\pi+9$

$2\pi ^2-3$

Correct answer:

$2\pi ^2-3\pi$

Explanation:

Write the formula for the circumference of the circle.

$C=2\pi r = \pi D$

Substitute the diameter.

$C= \pi (2\pi-3) = 2\pi ^2-3\pi$

The answer is: $2\pi ^2-3\pi$

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Example Question #82 : Geometry And Graphs

Determine the circumference of the circle with a diameter of $\frac{5}{3}$ .

Possible Answers:

$\frac{5}{3} \pi$

$\frac{25}{9} \pi$

$\frac{25}{3} \pi$

$\frac{25}{6} \pi$

$\frac{5}{6} \pi$

Correct answer:

$\frac{5}{3} \pi$

Explanation:

Write the formula for the circumference of the circle.

$C= 2\pi r = \pi D$

Substitute the diameter.

$C = \pi(\frac{5}{3})$

The answer is: $\frac{5}{3} \pi$

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Example Question #81 : Geometry And Graphs

You have a giant gong that has a diameter of 1.5 m . Find the circumference of the gong.

Possible Answers:

2.36 m

2.25m

4.71m

9.42m

Correct answer:

4.71m

Explanation:

You have a giant gong that has a diameter of 1.5 m . Find the circumference of the gong.

To find the circumference of a circle, simply use the following formula:

$Circ=2\pi r=d \pi$

So, if we plug in our diameter, we get:

$C=\pi (1.5m)=4.71 m$

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Example Question #85 : Geometry And Graphs

While doing your homework, you become distracted by the 3 holes on the margin of your paper. You estimate that the holes have a diameter of 2.5 cm. What is the circumference of the circles?

Possible Answers:

19.63 cm

4.91 cm

7.85cm

5cm

Correct answer:

7.85cm

Explanation:

While doing your homework, you become distracted by the 3 holes on the margin of your paper. You estimate that the holes have a diameter of 2.5 cm. What is the circumference of the circles?

To find circumference, use the following formula:

$C=2 \pi r$

Now, we could find the radius and then plug it in, but if you are astute, you will see that the above formula is the same thing as:

$C= \pi d$

Where d is the diameter.

So, we can plug in our diameter to find our answer:

$C= \pi (2.5cm)\approx 7.85cm$

So we can say our answer is 7.85 cm

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Example Question #86 : Geometry And Graphs

Find the area of a circle that has a circumference of $26\pi$ .

Possible Answers:

$130\pi$

$52\pi$

$13\pi$

$169\pi$

Correct answer:

$169\pi$

Explanation:

Recall how to find the circumference of a circle:

$\text{Circumference}=2\pi r$ , where is the radius.

Using the given circumference, solve for .

$26\pi=2\pi r$

r=13

Now, recall how to find the area of a circle:

$\text{Area}=\pi r^2$

Plug in the radius to find the area.

$\text{Area}=\pi (13)^2=169\pi$

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Example Question #87 : Geometry And Graphs

Find the circumference of a circle with an area of $36\pi.$

Possible Answers:

$6 \pi$

$12\pi$

$36 \pi$

$2 \pi$

$18 \pi$

Correct answer:

$12\pi$

Explanation:

The problem is asking for us to solve for the circumference. However, the only provided information is the circle's area. In this kind of a problem, it's important think about how the provided information may relate to the information we need in order to solve for the problem.

The area of a circle is determined through the formula: $A=\pi r^2$ , where r is for radius.

The circumference of a circle is determined by the formula: $C= \pi d$ where d is diameter. It can also be written as $C=2\pi r$ because the radius is half the length of the diameter.

We can now easily see that the two concepts, area and circumference, are related through the variable r. Therefore, if we can solve for r from the area, we can use that to then solve for circumference.

$36\pi = \pi r^2$

$\frac{36 \pi}{\pi} = r^2$

36=r^2

r=6

Now that we have solved for the radius, we can use this value to "plug and chug" into the circumference formula and solve.

$C= 2 \pi (6)$

$C= 12 \pi$

Therefore, the circumference of the circle is $12\pi$ .

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Example Question #88 : Geometry And Graphs

What is the circumference of a circle with an area of $49\pi$ ?

Possible Answers:

$12 \pi$

$24.5 \pi$

$7 \pi$

$13\pi$

$14\pi$

Correct answer:

$14\pi$

Explanation:

The area of a circle is determined through the formula: $A=\pi r^2$ , where r is for radius.

The circumference of a circle is determined by the formula: $C= \pi d$ where d is diameter. It can also be written as $C=2\pi r$ because the radius is half the length of the diameter.

$49\pi = \pi r^2$

$\frac{49 \pi}{\pi} = r^2$

49=r^2

r=7

Now that we have solved for the radius, we can use this value to "plug and chug" into the circumference formula and solve.

$C= 2 \pi (7)$

$C= 14 \pi$

Therefore, the circumference of the circle is $14\pi$ .

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Example Question #89 : Geometry And Graphs

Find the circumference of a circle with an area of $196 \pi$ .

Possible Answers:

$14 \pi$

$28\pi$

$46 \pi$

$23 \pi$

$7 \pi$

Correct answer:

$28\pi$

Explanation:

The area of a circle is determined through the formula: $A=\pi r^2$ , where r is for radius.

The circumference of a circle is determined by the formula: $C= \pi d$ where d is diameter. It can also be written as $C=2\pi r$ because the radius is half the length of the diameter.

$196\pi = \pi r^2$

$\frac{196 \pi}{\pi} = r^2$

196=r^2

r=14

Now that we have solved for the radius, we can use this value to "plug and chug" into the circumference formula and solve.

$C= 2 \pi (14)$

$C= 28 \pi$

Therefore, the circumference of the circle is $28\pi$ .

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Example Question #90 : Geometry And Graphs

If a circle has a diameter of , what is its circumference?

Possible Answers:

18.3

27.9

33.7

31.4

64.2

Correct answer:

31.4

Explanation:

The problem is asking for us to solve for the circumference. However, the only provided information is the circle's diameter. In this kind of a problem, it's important think about how the provided information may relate to the information we need in order to solve for the problem.

The circumference of a circle is determined by the formula: $C=2\pi r$ where r is radius. It can also be written as $C= \pi d$ because the diameter is twice the length of the radius.

We can now easily see that the two concepts, diameter and circumference, are related. Therefore, we just need to substitute the diameter value into the circumference formula to solve.

$C=10 \cdot \pi$

$C= 10 \pi$

C=31.4

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GED Math : Geometry and Graphs

Study concepts, example questions & explanations for GED Math

All GED Math Resources

Example Questions

Example Question #81 : Geometry And Graphs

Example Question #81 : Geometry And Graphs

Example Question #82 : Geometry And Graphs

Example Question #81 : Geometry And Graphs

Example Question #85 : Geometry And Graphs

Example Question #86 : Geometry And Graphs

Example Question #87 : Geometry And Graphs

Example Question #88 : Geometry And Graphs

Example Question #89 : Geometry And Graphs

Example Question #90 : Geometry And Graphs

All GED Math Resources

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