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GED Math : Circles

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Example Questions

Example Question #1 : Circumference

Give the circumference of a circle with radius 6. Round to the nearest tenth.

Possible Answers:

75.4

113.0

18.8

452.2

37.7

Correct answer:

37.7

Explanation:

The circumference of a circle can be found using this formula:

$C = 2 \pi r$

Where $\pi \approx 3.14$

Substitute r = 6 and use $\pi = 3.14$ , since we are rounding:

$C = 2 \cdot 3.14 \cdot 6 = 37.68$

Round this to 37.7 .

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Example Question #2 : Circumference

A car whose tires have diameter 30 inches moves at a rate of 24 miles per hour. How many revolutions will each tire make in one minute (nearest whole number)?

Possible Answers:

111

3,227

134

269

Correct answer:

269

Explanation:

We will convert all linear distances to feet and all times to minutes.

The tires have diameter 30 inches, which is equal to $30 \div 12 = 2.5$ feet. Their circumference will be $\pi$ times this, or $2.5 \pi$ feet.

The car moves at a rate of 25 miles per hour, which is equivalent to

$24 \times \frac{5,280}{ 60} = 2,112$ feet per minute.

The number of revolutions each tire makes is the distance traveled divided by the circumference of the tire, which is

$\frac{ 2,112 }{2.5 \pi} \approx \frac{ 2,112 }{7.8540} \approx 269$ .

Each tire revolves about 269 times in the course of one minute.

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Example Question #1 : Circumference

What is the circumference of a circle given the radius is 7?

Possible Answers:

$21\pi$

$10\pi$

$14\pi$

$7\pi$

Correct answer:

$14\pi$

Explanation:

The equation of circumference of a circle can be found using $C=2\pi r$ . By substituting in our radius of 7 we can solve for C.

$C=2(7)\pi$

$C=14\pi$

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Example Question #2 : Circumference

What is the circumference of a circle with a diameter of 10 inches?

Possible Answers:

13.5

15.7

31.4

Correct answer:

31.4

Explanation:

The equation for the circumference of a circle is $C=2r\pi$ , where is the radius of the circle. The radius is half the diameter, or 5 inches.

$C=2(5)\pi$

$C=10\pi$

$\pi=3.14$

C=10(3.14)

C=31.4

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Example Question #5 : Circumference

What is the circumference of a circle with radius 3?

Possible Answers:

18.84

12.87

9.14

6.45

Correct answer:

18.84

Explanation:

The equation for circumference of a circle is $C=2\pi r$ .

Plug in the given radius value and solve:

$C=2(3)\pi$

C=2(3)(3.14)

C=18.84

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Example Question #3 : Circumference

What is the circumference of a circle with a diameter of 40?

Possible Answers:

$10\pi$

$20\pi$

$40\pi$

$30\pi$

Correct answer:

$40\pi$

Explanation:

To find the circumference given the diameter we use the equation:

$C=D\pi$

Then we substitute 40 in for our diameter:

$C=40\pi$

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Example Question #7 : Circumference

Find the radius of a circle given that the circumference is $24\pi$ .

Possible Answers:

Correct answer:

Explanation:

The equation of the circumference of a circle is as follows:

$C=2\pi r$

Now we substitute in our circumference and solve for radius:

$24\pi=2\pi r$

12=r

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Example Question #1 : Circumference

What is the circumference of a circle with a radius of 4?

Possible Answers:

$4\pi$

$12\pi$

$8\pi$

$16\pi$

Correct answer:

$8\pi$

Explanation:

We use the equation for the circumference of a circle: $C=2\pi r$

Now we substitute in our radius of 4:

$C=2(4)\pi$

$C=8\pi$

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Example Question #9 : Circumference

If the area of a circle is $81\pi$ , what is its circumference?

Possible Answers:

$18\pi$

$324\pi$

$27\pi$

$9\pi$

Cannot be computed from the information provided

Correct answer:

$18\pi$

Explanation:

To solve this, you should first figure out your radius. Remember that the area of a circle is defined as:

$A=\pi r^2$

For your data, you know that this is:

$81\pi=\pi r^2$

Solving for , you get:

81=r^2 , or

r=9

Now, recall that the circumference of a circle is defined as:

$C=2\pi r$

For your data, this is:

$C=2\pi * 9 = 18\pi$

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Example Question #10 : Circumference

The area of a sector of a circle with a degree angle is $4\pi$ . What is the circumference of this circle?

Possible Answers:

$4\pi$

$12\pi$

$8\pi$

Cannot be computed from the information provided

$16\pi$

Correct answer:

$8\pi$

Explanation:

A degree angle represents one fourth of a full circle. Therefore, the total area of this circle is $4 * 4\pi$ or $16\pi$ . Now, recall your area formula:

$A=\pi r^2$

For your data, this means:

$16\pi = \pi r^2$

Solving for , you get:

16=r^2 or r=4

Now, the circumference of a circle is defined as:

$C=2\pi r$

For your data, this is:

$C=2*4*\pi=8\pi$

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GED Math : Circles

Study concepts, example questions & explanations for GED Math

All GED Math Resources

Example Questions

Example Question #1 : Circumference

Example Question #2 : Circumference

Example Question #1 : Circumference

Example Question #2 : Circumference

Example Question #5 : Circumference

Example Question #3 : Circumference

Example Question #7 : Circumference

Example Question #1 : Circumference

Example Question #9 : Circumference

Example Question #10 : Circumference

All GED Math Resources

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