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GED Math : Geometry and Graphs

Study concepts, example questions & explanations for GED Math

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

Example Questions

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: $4\pi \sqrt{3}$

Report an Error

Example Question #14 : Circumference

What is the circumference of a circle with a diameter of $2\sqrt2$ ?

Possible Answers:

$4\pi$

$2\sqrt2$

$8\pi$

$2\pi \sqrt{2}$

$4\pi \sqrt{2}$

Correct answer:

$2\pi \sqrt{2}$

Explanation:

Write the formula for the circumference of a circle.

$C=\pi D$

Substitute the diameter into the equation.

$C=\pi 2\sqrt2$

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

Report an Error

Example Question #15 : Circumference

Determine the circumference of a circle with a radius of $\frac{\pi}{4}$ .

Possible Answers:

$\frac{\pi ^2}{2}$

$\frac{\pi}{8}$

$\frac{1}{2}$

$\frac{\pi }{2}$

$\frac{\pi^2}{8}$

Correct answer:

$\frac{\pi ^2}{2}$

Explanation:

Write the formula for the circumference of a circle.

$C=\2\pi r$

Substitute the radius.

$C=\2\pi (\frac{\pi}{4}) = \frac{\pi ^2}{2}$

The answer is: $\frac{\pi ^2}{2}$

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Example Question #51 : Geometry And Graphs

Find the circumference of a circle with a diameter of 9cm.

Possible Answers:

$81\pi \text{ cm}$

$27\pi \text{ cm}$

$36\pi \text{ cm}$

$9\pi \text{ cm}$

$18\pi \text{ cm}$

Correct answer:

$9\pi \text{ cm}$

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 9cm. So, we will substitute. We get

$C = \pi \cdot 9\text{cm}$

$C = 9\pi \text{ cm}$

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Example Question #16 : Circumference

What is the circumference of a circle with an area of $12\pi$ ?

Possible Answers:

$\pi\sqrt{3}$

$2\pi\sqrt{3}$

$4\pi\sqrt{3}$

$2\sqrt{3}$

$6\pi\sqrt{3}$

Correct answer:

$4\pi\sqrt{3}$

Explanation:

For this question, you need to first use the area to calculate your circle's radius. From that, you can then calculate the circumference of the circle. Recall that the area of a circle is defined as:

$A=\pi r^2$

For your data, this means:

$12\pi=\pi r^2$

Solving for , you get...

12=r^2

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

Now, the circumference of a circle is calculated as:

$C=2\pi r$

For your data, this is:

$C=2\pi*2\sqrt{3}=4\pi\sqrt{3}$

Report an Error

Example Question #56 : Geometry And Graphs

Evaluate the circumference of a circle if the radius is $\frac{3}{4}$ .

Possible Answers:

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

$2\pi$

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

$3\pi$

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

Correct answer:

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

Explanation:

Write the equation for the circumference of a circle.

$C=2\pi r$

Substitute the radius and solve.

$C=2\pi (\frac{3}{4}) = \frac{6}{4}\pi = \frac{3}{2}\pi$

The answer is: $\frac{3}{2}\pi$

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All GED Math Resources

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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 #51 : Geometry And Graphs

Example Question #11 : Circumference

Example Question #12 : Circumference

Example Question #13 : Circumference

Example Question #51 : Geometry And Graphs

Example Question #14 : Circumference

Example Question #15 : Circumference

Example Question #51 : Geometry And Graphs

Example Question #16 : Circumference

Example Question #56 : Geometry And Graphs

All GED Math Resources

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