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GED Math : GED Math

Study concepts, example questions & explanations for GED Math

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All GED Math Resources

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

Example Questions

Example Question #1011 : Ged Math

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

Possible Answers:

$20\pi$

$40\pi$

$30\pi$

$10\pi$

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 #46 : Geometry And Graphs

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

Possible Answers:

$4\pi$

$12\pi$

$16\pi$

$8\pi$

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 #8 : Circumference

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

Possible Answers:

$324\pi$

$9\pi$

$18\pi$

$27\pi$

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 #9 : 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:

$8\pi$

$12\pi$

$16\pi$

$4\pi$

Cannot be computed from the information provided

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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Example Question #51 : Geometry And Graphs

What is the circumference of the circle with an area of 5?

Possible Answers:

$2\sqrt{5\pi}$

$2\pi \sqrt{5\pi}$

$\sqrt{10\pi}$

$10\sqrt{\pi}$

$\textup{The answer is not given.}$

Correct answer:

$2\sqrt{5\pi}$

Explanation:

Write the formula for the area of a circle.

$A =\pi r^2$

Substitute the area.

$5 =\pi r^2$

Divide by pi on both sides.

$\frac{5}{\pi } =\frac{\pi r^2}{\pi }$

$r^2 = \frac{5}{\pi}$

Square root both sides.

$\sqrt{r^2} = \sqrt{\frac{5}{\pi}}$

$r = \sqrt{\frac{5}{\pi}}$

Write the circumference formula for the circle, and substitute the radius.

$C=2\pi r =2\pi \sqrt{\frac{5}{\pi}} = 2\pi \frac{\sqrt{5}}{\sqrt{\pi}}$

Since $\pi = (\sqrt{\pi} \cdot \sqrt{\pi})$ , we can eliminate the denominator by rewriting $\pi$ .

$2\pi \frac{\sqrt{5}}{\sqrt{\pi}} = 2(\sqrt{\pi}\cdot \sqrt{\pi}) \frac{\sqrt{5}}{\sqrt{\pi}} = 2\sqrt{\pi}\cdot \sqrt{5}$

The answer is: $2\sqrt{5\pi}$

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Example Question #11 : Circumference

Find the circumference of a circle with an area of $12\pi$ .

Possible Answers:

$4\pi \sqrt3$

$2\pi \sqrt6$

$3\pi \sqrt{2}$

$2\pi \sqrt3$

$4\pi$

Correct answer:

$4\pi \sqrt3$

Explanation:

Write the formula for the area of a circle, and substitute the area into the formula.

$A=\pi r^2$

$12\pi =\pi r^2$

Divide by pi on both sides.

$\frac{12\pi }{\pi}=\frac{\pi r^2}{\pi}$

r^2 = 12

Square root both sides.

$\sqrt{r^2 }= \sqrt{12}$

$r=2\sqrt{3}$

Write the formula for the circumference of the circle.

$C=2\pi r$

Substitute the radius into the equation.

$C=2\pi (2\sqrt3) = 4\pi \sqrt3$

The answer is: $4\pi \sqrt3$

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Example Question #12 : Circumference

Find the circumference of a circle with a diameter of $5\pi^2$ .

Possible Answers:

$5\pi ^3$

$\frac{25}{4}\pi ^4$

$10\pi ^3$

$10\pi ^2$

$\frac{25}{4}\pi ^3$

Correct answer:

$5\pi ^3$

Explanation:

Write the formula for the circumference.

$C=\pi D$

Substitute the diameter into the equation.

$C=\pi (5\pi^2) = 5\pi ^3$

The answer is: $5\pi ^3$

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Example Question #13 : Circumference

Find the circumference of a circle with a diameter of 14cm.

Possible Answers:

$14\pi \text{ cm}$

$49\pi \text{ cm}$

$196\pi \text{ cm}$

$7\pi \text{ cm}$

$28\pi \text{ cm}$

Correct answer:

$14\pi \text{ cm}$

Explanation:

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

$C = \pi d$

where d is the diameter of the circle.

Now, we know the diameter of the circle is 14cm. So, we will substitute. We get

$C = \pi \cdot 14\text{cm}$

$C = 14\pi \text{ cm}$

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Example Question #51 : Geometry And Graphs

Identify the circumference of the circle with an area of $12 \pi$ .

Possible Answers:

$\frac{3\pi \sqrt{3}}{2}$

$\frac{2\pi \sqrt{3}}{3}$

$2\pi \sqrt{3}$

$\frac{4\pi \sqrt{3}}{3}$

$4\pi \sqrt{3}$

Correct answer:

$4\pi \sqrt{3}$

Explanation:

Write the formula for the area of a circle.

$A=\pi r^2$

Substitute the area.

$12\pi=\pi r^2$

r^2=12

Square root both sides to find the radius.

$\sqrt{r^2}=\sqrt{12}$

$r=\sqrt{12} = \sqrt{4}\times \sqrt{3} = 2\sqrt{3}$

Write the formula for the circumference of the circle.

$C=2\pi r = 2\pi(2\sqrt{3}) = 4\pi \sqrt{3}$

The answer is: $4\pi \sqrt{3}$

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GED Math : GED Math

Study concepts, example questions & explanations for GED Math

All GED Math Resources

Example Questions

Example Question #1011 : Ged Math

Example Question #7 : Circumference

Example Question #46 : Geometry And Graphs

Example Question #8 : Circumference

Example Question #9 : Circumference

Example Question #51 : Geometry And Graphs

Example Question #11 : Circumference

Example Question #12 : Circumference

Example Question #13 : Circumference

Example Question #51 : Geometry And Graphs

All GED Math Resources

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