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Common Core: 7th Grade Math : Area of a circle

Study concepts, example questions & explanations for Common Core: 7th Grade Math

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All Common Core: 7th Grade Math Resources

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Example Questions

Example Question #1 : Area Of A Circle

What is the area of a circle that has a diameter of inches?

Possible Answers:

960

153.938

706.8583

153.938

176.7146

960

940

Correct answer:

176.7146

Explanation:

The formula for finding the area of a circle is $\pi r^{2}$ . In this formula, represents the radius of the circle. Since the question only gives us the measurement of the diameter of the circle, we must calculate the radius. In order to do this, we divide the diameter by .

$\frac{15}{2}=7.5$

Now we use 7.5 for in our equation.

$\pi (7.5)^{2}=176.7146 \: in^{2}$

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Example Question #1 : Area Of A Circle

What is the area of a circle with a diameter equal to 6?

Possible Answers:

$3\pi$

$9\pi$

$18\pi$

$36\pi$

Correct answer:

$9\pi$

Explanation:

First, solve for radius:

$r=\frac{d}{2}=\frac{6}{2}=3$

Then, solve for area:

$A=r^2\pi=3^2\pi=9\pi$

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Example Question #1 : Area Of A Circle

The diameter of a circle is $4\ cm$ . Give the area of the circle.

Possible Answers:

$12 \ cm^2$

$11.56\ cm^2$

$13\ cm^2$

$13.56\ cm^2$

$12.56\ cm^2$

Correct answer:

$12.56\ cm^2$

Explanation:

The area of a circle can be calculated using the formula:

$Area=\frac{\pi d^2}{4}$ ,

where is the diameter of the circle, and $\pi$ is approximately 3.14 .

$Area=\frac{\pi d^2}{4}=\frac{\pi\times 4^2}{4}=4\pi \Rightarrow Area\approx 4\times 3.14\Rightarrow Area\approx 12.56 \ cm^2$

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Example Question #2 : Area Of A Circle

The diameter of a circle is . Give the area of the circle in terms of .

Possible Answers:

11.56 t^2

12.56 t

12.56 t^2

12 t^2

11.56 t

Correct answer:

12.56 t^2

Explanation:

The area of a circle can be calculated using the formula:

$Area=\frac{\pi d^2}{4}$ ,

where is the diameter of the circle and $\pi$ is approximately 3.14 .

$Area=\frac{\pi (4t)^2}{4}=\frac{16\pi t^2}{4}=4\pi t^2 \Rightarrow Area\approx 4\times 3.14\times t^2$

$\Rightarrow Area\approx 12.56t^2$

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Example Question #3 : How To Find The Area Of A Circle

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

Possible Answers:

$4\pi$

$2\pi$

$\frac{4}{\pi }$

Correct answer:

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 3.14 .

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

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Example Question #3 : Area Of A Circle

The circumference of a circle is 12.56 inches. Find the area of the circle.

Let $\pi = 3.14$ .

Possible Answers:

$12\ in^2$

$11.56\ in^2$

$12.56\ in^2$

$11\ in^2$

$13.56\ in^2$

Correct answer:

$12.56\ in^2$

Explanation:

First we need to find the radius of the circle. The circumference of a circle is $Circumference =2\pi r$ , where is the radius of the circle.

$12.56=2\times 3.14\times r\Rightarrow r=2\ in$

The area of a circle is $Area=\pi r^2$ where is the radius of the circle.

$Area=\pi r^2=3.14\times 2^2=12.56\ in^2$

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Example Question #1 : Radius

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

Possible Answers:

$58.7\ cm^{2}$

$78\ cm^{2}$

$28.3\ cm^{2}$

$12.6\ cm^{2}$

$50.2\ cm^{2}$

Correct answer:

$50.2\ cm^{2}$

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 $50.2\ cm^{2}$ .

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Example Question #1 : Plane Geometry

The radius, , of the circle below is 18 units. What is the area of the circle?

Circle

Possible Answers:

324 square units

$18\pi$ square units

$36\pi$ square units

$324\pi$ square units

Cannot be determined

Correct answer:

$324\pi$ square units

Explanation:

The formula for the area, , of a circle with radius is:

$A=\pi R^{2}$

We can fill in

$A=\pi (18^{2})$

$A=324\pi$

You could do the arithmetic to get an area of about 1,017.876 square units, but it is ok and more precise to leave it as shown.

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Example Question #1 : Circles

Give the area of a circle with diameter 13.

Possible Answers:

$\frac{169\pi }{2}$

$\frac{13\pi }{2}$

$26 \pi$

$13 \pi$

$\frac{169\pi }{4}$

Correct answer:

$\frac{169\pi }{4}$

Explanation:

Half of the diameter 13 is the radius $\frac{13}{2}$ . Use the area formula:

$A = \pi r^{2} = \pi \cdot \left ( \frac{13}{2} \right )^{2} = \frac{169\pi }{4}$

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Example Question #25 : Radius

How many times greater is the area of a circle with a radius of 4in., compared to a circle with a radius of 2in.?

Possible Answers:

$\pi$

$4$

$2\pi$

$4\pi$

$2$

Correct answer:

$4$

Explanation:

The area of a circle can be solved using the equation $A=\pi r^{2}$

The area of a circle with radius 4 is $\pi 4^{2}=16\pi$ while the area of a circle with radius 2 is $\pi 2^{2}=4\pi$ . $16\pi \div 4\pi =4$

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Common Core: 7th Grade Math : Area of a circle

Study concepts, example questions & explanations for Common Core: 7th Grade Math

All Common Core: 7th Grade Math Resources

Example Questions

Example Question #1 : Area Of A Circle

Example Question #1 : Area Of A Circle

Example Question #1 : Area Of A Circle

Example Question #2 : Area Of A Circle

Example Question #3 : How To Find The Area Of A Circle

Example Question #3 : Area Of A Circle

Example Question #1 : Radius

Example Question #1 : Plane Geometry

Example Question #1 : Circles

Example Question #25 : Radius

All Common Core: 7th Grade Math Resources

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