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

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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 $\displaystyle 15$ inches?

Possible Answers:

$\displaystyle 706.8583$

153.938 $\displaystyle 153.938$

$\displaystyle 176.7146$

940 $\displaystyle 940$

153.938 $\displaystyle 153.938$

940 $\displaystyle 940$

960 $\displaystyle 960$

Correct answer:

$\displaystyle 176.7146$

Explanation:

The formula for finding the area of a circle is $\pi r^{2}$ $\displaystyle \pi r^{2}$. In this formula, $\displaystyle r$ 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 $\displaystyle 2$.

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

Now we use 7.5 $\displaystyle 7.5$ for $\displaystyle r$ in our equation.

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

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Example Question #3 : Area Of A Circle

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

Possible Answers:

$18\pi$ $\displaystyle 18\pi$

$36\pi$ $\displaystyle 36\pi$

$9\pi$ $\displaystyle 9\pi$

$3\pi$ $\displaystyle 3\pi$

Correct answer:

$9\pi$ $\displaystyle 9\pi$

Explanation:

First, solve for radius:

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

Then, solve for area:

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

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Example Question #1 : Know And Use The Formulas For The Area And Circumference Of A Circle: Ccss.Math.Content.7.G.B.4

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

Possible Answers:

$12.56\ cm^2$ $\displaystyle 12.56\ cm^2$

$11.56\ cm^2$ $\displaystyle 11.56\ cm^2$

$13.56\ cm^2$ $\displaystyle 13.56\ cm^2$

$13\ cm^2$ $\displaystyle 13\ cm^2$

$12 \ cm^2$ $\displaystyle 12 \ cm^2$

Correct answer:

$12.56\ cm^2$ $\displaystyle 12.56\ cm^2$

Explanation:

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

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

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

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

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Example Question #2 : Know And Use The Formulas For The Area And Circumference Of A Circle: Ccss.Math.Content.7.G.B.4

The diameter of a circle is $\displaystyle 4t$. Give the area of the circle in terms of $\displaystyle t$.

Possible Answers:

12 t^2 $\displaystyle 12 t^2$

12.56 t $\displaystyle 12.56 t$

$\displaystyle 11.56 t^2$

$\displaystyle 12.56 t^2$

11.56 t $\displaystyle 11.56 t$

Correct answer:

$\displaystyle 12.56 t^2$

Explanation:

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

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

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

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

$\Rightarrow Area\approx 12.56t^2$ $\displaystyle \Rightarrow Area\approx 12.56t^2$

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Example Question #1 : How To Find The Area Of A Circle

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

Possible Answers:

$2\pi$ $\displaystyle 2\pi$

$\displaystyle 2$

$\frac{4}{\pi }$ $\displaystyle \frac{4}{\pi }$

$\displaystyle 4$

$4\pi$ $\displaystyle 4\pi$

Correct answer:

$\displaystyle 4$

Explanation:

The area of a circle can be calculated as $Area=\pi r^2$ $\displaystyle Area=\pi r^2$, where $\displaystyle r$ is the radius of the circle, and $\pi$ $\displaystyle \pi$ is approximately 3.14 $\displaystyle 3.14$.

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

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Example Question #5 : Area Of A Circle

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

Let $\pi = 3.14$ $\displaystyle \pi = 3.14$.

Possible Answers:

$11.56\ in^2$ $\displaystyle 11.56\ in^2$

$11\ in^2$ $\displaystyle 11\ in^2$

$13.56\ in^2$ $\displaystyle 13.56\ in^2$

$12.56\ in^2$ $\displaystyle 12.56\ in^2$

$12\ in^2$ $\displaystyle 12\ in^2$

Correct answer:

$12.56\ in^2$ $\displaystyle 12.56\ in^2$

Explanation:

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

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

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

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

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Example Question #1 : Area Of A Circle

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

Possible Answers:

$12.6\ cm^{2}$ $\displaystyle 12.6\ cm^{2}$

$50.2\ cm^{2}$ $\displaystyle 50.2\ cm^{2}$

$78\ cm^{2}$ $\displaystyle 78\ cm^{2}$

$58.7\ cm^{2}$ $\displaystyle 58.7\ cm^{2}$

$28.3\ cm^{2}$ $\displaystyle 28.3\ cm^{2}$

Correct answer:

$50.2\ cm^{2}$ $\displaystyle 50.2\ cm^{2}$

Explanation:

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

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

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

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Example Question #1 : Area Of A Circle

The radius, $\displaystyle R$, of the circle below is 18 units. What is the area of the circle?

Circle

Possible Answers:

$324\pi$ $\displaystyle 324\pi$ square units

Cannot be determined

$18\pi$ $\displaystyle 18\pi$ square units

324 $\displaystyle 324$ square units

$36\pi$ $\displaystyle 36\pi$ square units

Correct answer:

$324\pi$ $\displaystyle 324\pi$ square units

Explanation:

The formula for the area, $\displaystyle A$, of a circle with radius $\displaystyle R$ is:

$A=\pi R^{2}$ $\displaystyle A=\pi R^{2}$

We can fill in $\displaystyle R$

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

$A=324\pi$ $\displaystyle A=324\pi$

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 : Basic Geometry

Give the area of a circle with diameter 13.

Possible Answers:

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

$13 \pi$ $\displaystyle 13 \pi$

$26 \pi$ $\displaystyle 26 \pi$

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

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

Correct answer:

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

Explanation:

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

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

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Example Question #21 : How To Find The Area Of A Circle

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:

$4$ $\displaystyle 4$

$2\pi$ $\displaystyle 2\pi$

$2$ $\displaystyle 2$

$\pi$ $\displaystyle \pi$

$4\pi$ $\displaystyle 4\pi$

Correct answer:

$4$ $\displaystyle 4$

Explanation:

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

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

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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 #3 : Area Of A Circle

Example Question #1 : Know And Use The Formulas For The Area And Circumference Of A Circle: Ccss.Math.Content.7.G.B.4

Example Question #2 : Know And Use The Formulas For The Area And Circumference Of A Circle: Ccss.Math.Content.7.G.B.4

Example Question #1 : How To Find The Area Of A Circle

Example Question #5 : Area Of A Circle

Example Question #1 : Area Of A Circle

Example Question #1 : Area Of A Circle

Example Question #1 : Basic Geometry

Example Question #21 : How To Find The Area Of A Circle

All Common Core: 7th Grade Math Resources

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