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GED Math : Circles

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

Example Questions

Example Question #25 : Area Of A Circle

Find the area of a circle with a diameter of $\frac{3}{2}$ .

Possible Answers:

$\frac{9}{16}\pi$

$9\pi$

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

$\frac{9}{2}\pi$

$\frac{9}{4}\pi$

Correct answer:

$\frac{9}{16}\pi$

Explanation:

Write the formula for the area of a circle.

$A = \pi r^2$

The radius is half the diameter.

Multiply the diameter by $\frac{1}{2}$ .

$\frac{1}{2} \times \frac{3}{2} = \frac{3}{4}$

Substitute the radius.

$A = \pi (\frac{3}{4})^2 = \pi (\frac{3}{4})(\frac{3}{4}) = \frac{9}{16}\pi$

The answer is: $\frac{9}{16}\pi$

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Example Question #121 : Circles

Find the area of a circle with a diameter of $5\pi$ .

Possible Answers:

$\frac{25}{4}\pi^2$

$\frac{25}{2}\pi^3$

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

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

$\frac{25}{2}\pi^2$

Correct answer:

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

Explanation:

Write the area of a circle.

$A=\pi r^2$

The radius is half the diameter.

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

Substitute the radius into the equation.

$A=\pi (\frac{5\pi}{2})^2=\pi (\frac{5\pi}{2})(\frac{5\pi}{2})$

The answer is: $\frac{25}{4}\pi^3$

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Example Question #121 : 2 Dimensional Geometry

Circle 1

Give the area of the above circle.

Possible Answers:

$\frac{49 }{4}\pi$

$7 \pi$

$14 \pi$

$49 \pi$

Correct answer:

$\frac{49 }{4}\pi$

Explanation:

The area of a circle, given its radius , can be found using the formula

$A = \pi r^{2}$

The radius is half the diameter - that is, $r = \frac{d}{2}$ - so, substituting,

$A = \pi \left ( \frac{d}{2} \right )^{2}$

$A = \pi \left ( \frac{d^{2}}{2^{2}} \right )$

$A = \left ( \frac{d^{2}}{4} \right )\pi$

The diameter of the given circle is 7, so set d=7 in the above formula:

$A = \left ( \frac{7^{2}}{4} \right )\pi$

$A = \frac{49}{4} \pi$ ,

the correct area.

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Example Question #124 : Geometry And Graphs

Let $\pi=3.14$ .

Find the area of a circle with a diameter of 12in.

Possible Answers:

$40.80\text{in}^2$

$37.68\text{in}^2$

$113.04\text{in}^2$

$452.16\text{in}^2$

$56.52\text{in}^2$

Correct answer:

$113.04\text{in}^2$

Explanation:

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

$A = \pi \cdot r^2$

where r is the radius of the circle.

Now, we know $\pi=3.14$ . We also know the diameter is 12in. We know the diameter is two times the radius, so the radius is 6in. Now, we can substitute. We get

$A = 3.14 \cdot (6\text{in})^2$

$A = 3.14 \cdot 36\text{in}^2$

$A = 113.04\text{in}^2$

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Example Question #122 : Circles

What is the area of a circle with a circumference of $3\pi$ ?

Possible Answers:

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

$9\pi$

$6\pi$

$\frac{9}{4}\pi$

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

Correct answer:

$\frac{9}{4}\pi$

Explanation:

Write the formula for the area of a circle.

$A=\pi r^2$

We will need to find the radius of the circle.

Write the formula for the circumference.

$C=2\pi r$

Substitute the circumference.

$3\pi=2\pi r$

Divide by $2\pi$ on both sides.

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

The radius is: $\frac{3}{2}$

Substitute this into the area formula.

$A=\pi (\frac{3}{2})^2 = \frac{9}{4}\pi$

The answer is: $\frac{9}{4}\pi$

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Example Question #29 : Area Of A Circle

Find the area of the circle with radius of 9x^3 .

Possible Answers:

$81\pi^2 x^6$

$81\pi x^9$

$81\pi x^6$

$81\pi^2 x^9$

9x^6

Correct answer:

$81\pi x^6$

Explanation:

Write the formula for the area of a circle.

$A=\pi r^2$

Substitute the radius.

$A=\pi (9x^3)^2=\pi (9x^3)(9x^3) = 81\pi x^6$

The answer is: $81\pi x^6$

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Example Question #121 : 2 Dimensional Geometry

Find the area of the circle with a radius of $\pi ^3$ .

Possible Answers:

$\pi ^{10}$

$\pi ^7$

$\pi ^4$

$\pi ^9$

$\pi^6$

Correct answer:

$\pi ^7$

Explanation:

Write the formula for the area of a circle.

$A=\pi r^2$

Substitute the radius.

$A=\pi( \pi^3)^2 = \pi( \pi^3)( \pi^3) = \pi ^7$

The answer is: $\pi ^7$

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Example Question #31 : Area Of A Circle

Find the area of a circle with a diameter of 2x^2 .

Possible Answers:

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

4x^2

$\pi x^3$

2x^4

$\pi x^4$

Correct answer:

$\pi x^4$

Explanation:

The radius of the circle is half the diameter, or x^2 .

Write the formula for the area of the circle.

$A= \pi r^2$

Substitute the radius.

$A= \pi (x^2)^2 = \pi (x^2)(x^2) = \pi x^4$

The answer is: $\pi x^4$

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Example Question #32 : Area Of A Circle

Determine the area of a circle with a diameter of $\pi^2$ .

Possible Answers:

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

$\frac{\pi^5}{4}$

$\pi^4$

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

$\frac{\pi^4}{2}$

Correct answer:

$\frac{\pi^5}{4}$

Explanation:

The radius of the circle is half the diameter, or $\frac{\pi^2}{2}$ .

Write the formula for the area of a circle.

$A = \pi r^2$

Substitute the radius.

$A = \pi (\frac{\pi^2}{2})^2= \pi (\frac{\pi^2}{2})(\frac{\pi^2}{2})$

The answer is: $\frac{\pi^5}{4}$

Report an Error

Example Question #33 : Area Of A Circle

Determine the area of a circle with a radius of 16x .

Possible Answers:

$32\pi x^2$

$256\pi x^2$

$256\pi x$

32x^2

$216\pi x^2$

Correct answer:

$256\pi x^2$

Explanation:

Write the area of a circle.

$A =\pi r^2$

Substitute the radius into the equation.

$A =\pi (16x)^2=\pi (16x)(16x)$

The answer is: $256\pi x^2$

Report an Error

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GED Math : Circles

Study concepts, example questions & explanations for GED Math

All GED Math Resources

Example Questions

Example Question #25 : Area Of A Circle

Example Question #121 : Circles

Example Question #121 : 2 Dimensional Geometry

Example Question #124 : Geometry And Graphs

Example Question #122 : Circles

Example Question #29 : Area Of A Circle

Example Question #121 : 2 Dimensional Geometry

Example Question #31 : Area Of A Circle

Example Question #32 : Area Of A Circle

Example Question #33 : Area Of A Circle

All GED Math Resources

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