Know and Use the Formulas for the Area and Circumference of a Circle: CCSS.Math.Content.7.G.B.4

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7th Grade Math › Know and Use the Formulas for the Area and Circumference of a Circle: CCSS.Math.Content.7.G.B.4

Questions 1 - 10

1

If a circle has an area of $16\pi ; in^{2}$ , what is the circumference?

$8\pi ; in$

$12\pi ; in$

$4\pi ; in$

$6\pi ; in$

$10\pi ; in$

Explanation

For a circle, the formula for area is $A = \pi r^{2}$ and the formula for circumference is $C=\pi d$ , where is the radius and is the diameter.

Plug the known quantities into the area formula and solve for the radius:

$16\pi =\pi r^{2}$

Now plug this value into the circumference formula to solve:

$C = \pi d = \pi 2r = \pi 2(4) = 8\pi; in$

2

If a circle has an area of $16\pi ; in^{2}$ , what is the circumference?

$8\pi ; in$

$12\pi ; in$

$4\pi ; in$

$6\pi ; in$

$10\pi ; in$

Explanation

For a circle, the formula for area is $A = \pi r^{2}$ and the formula for circumference is $C=\pi d$ , where is the radius and is the diameter.

Plug the known quantities into the area formula and solve for the radius:

$16\pi =\pi r^{2}$

Now plug this value into the circumference formula to solve:

$C = \pi d = \pi 2r = \pi 2(4) = 8\pi; in$

3

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

$9\pi$

$81\pi$

$18\pi$

$27\pi$

$90\pi$

Explanation

The formula for the area of a circle is πr2. For this particular circle, the area is 81π, so 81π = πr2. Divide both sides by π and we are left with r2=81. Take the square root of both sides to find r=9. The formula for the circumference of the circle is 2πr = 2π(9) = 18π. The correct answer is 18π.

4

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

$9\pi$

$81\pi$

$18\pi$

$27\pi$

$90\pi$

Explanation

The formula for the area of a circle is πr2. For this particular circle, the area is 81π, so 81π = πr2. Divide both sides by π and we are left with r2=81. Take the square root of both sides to find r=9. The formula for the circumference of the circle is 2πr = 2π(9) = 18π. The correct answer is 18π.

5

The radius of a circle is 4 cm, what is the area?

$50.2\ cm^{2}$

$12.6\ cm^{2}$

$78\ cm^{2}$

$28.3\ cm^{2}$

$58.7\ cm^{2}$

Explanation

The area of a circle is found by: $Area=r^{2}\pi$ , where r is the radius.

$4^{2} \pi = 50.2$ .

The area of the circle is $50.2\ cm^{2}$ .

6

The radius of a circle is 4 cm, what is the area?

$50.2\ cm^{2}$

$12.6\ cm^{2}$

$78\ cm^{2}$

$28.3\ cm^{2}$

$58.7\ cm^{2}$

Explanation

The area of a circle is found by: $Area=r^{2}\pi$ , where r is the radius.

$4^{2} \pi = 50.2$ .

The area of the circle is $50.2\ cm^{2}$ .

7

The radius of a circle is $\frac{2}{\sqrt{\pi }}$ . Give the area of the circle.

$4\pi$

$\frac{4}{\pi }$

$2\pi$

Explanation

The area of a circle can be calculated as $Area=\pi r^2$ , where is the radius of the circle, and $\pi$ is approximately .

$Area=\pi r^2=\pi\times (\frac{2}{\sqrt{\pi}})^2=\pi\times \frac{4}{\pi}\Rightarrow Area=4$

8

What is the circumference of a circle with a radius of $5.2\textup{ in}$ ?

(Round your answer to the nearest tenth.)

$32.7\textup{ in}$

$10.4\textup{ in}$

$49.3\textup{ in}$

$22.8\textup{ in}$

$16.3\textup{ in}$

Explanation

The circumference is given by the formula:

$C=2\pi r$

where is the radius.

$2\pi (5.2)=32.7\ in$

9

The radius of a circle is $\frac{2}{\sqrt{\pi }}$ . Give the area of the circle.

$4\pi$

$\frac{4}{\pi }$

$2\pi$

Explanation

The area of a circle can be calculated as $Area=\pi r^2$ , where is the radius of the circle, and $\pi$ is approximately .

$Area=\pi r^2=\pi\times (\frac{2}{\sqrt{\pi}})^2=\pi\times \frac{4}{\pi}\Rightarrow Area=4$

10

What is the circumference of a circle with a radius of $5.2\textup{ in}$ ?

(Round your answer to the nearest tenth.)

$32.7\textup{ in}$

$10.4\textup{ in}$

$49.3\textup{ in}$

$22.8\textup{ in}$

$16.3\textup{ in}$

Explanation

The circumference is given by the formula:

$C=2\pi r$

where is the radius.

$2\pi (5.2)=32.7\ in$

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