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Pre-Algebra : Area

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Example Questions

Example Question #3 : Area Of A Circle

A circle has a diameter of $\displaystyle 10$ inches. What is the area of the circle? Round to the nearest tenth decimal place.

Possible Answers:

$78.5 \textup{ in}^2$ $\displaystyle 78.5 \textup{ in}^2$

$56.7 \textup{ in}^2$ $\displaystyle 56.7 \textup{ in}^2$

$314.3 \textup{ in}^2$ $\displaystyle 314.3 \textup{ in}^2$

$45.8 \textup{ in}^2$ $\displaystyle 45.8 \textup{ in}^2$

$75.4 \textup{ in}^2$ $\displaystyle 75.4 \textup{ in}^2$

Correct answer:

$78.5 \textup{ in}^2$ $\displaystyle 78.5 \textup{ in}^2$

Explanation:

The formula to find the area of a circle is $A=\pi\cdot r^2$ $\displaystyle A=\pi\cdot r^2$.

First you must find the radius from the diameter.

$r=\frac{1}{2}d \rightarrow r=\frac{1}{2}\cdot 10=5$ $\displaystyle r=\frac{1}{2}d \rightarrow r=\frac{1}{2}\cdot 10=5$

In this case it is,

$A=5^2 \cdot \pi = 25\cdot 3.14= 78.5$ $\displaystyle A=5^2 \cdot \pi = 25\cdot 3.14= 78.5$

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Example Question #2 : Area Of A Circle

What is the area of a circle that has a diameter of $\displaystyle 15$ inches?

Possible Answers:

153.938 $\displaystyle 153.938$

940 $\displaystyle 940$

153.938 $\displaystyle 153.938$

960 $\displaystyle 960$

940 $\displaystyle 940$

$\displaystyle 176.7146$

$\displaystyle 706.8583$

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 #4 : Area Of A Circle

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

Possible Answers:

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

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

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

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

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 #3 : Area Of A Circle

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

Possible Answers:

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

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

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

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

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

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 #5 : Area Of A Circle

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

Possible Answers:

$\displaystyle 11.56 t^2$

12.56 t $\displaystyle 12.56 t$

$\displaystyle 12.56 t^2$

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

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 #2 : 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:

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

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

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

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

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

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 #122 : Area

Find the area of a circle that has a radius of $\displaystyle 4$.

Possible Answers:

$16\pi$ $\displaystyle 16\pi$

$12\pi$ $\displaystyle 12\pi$

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

$8\pi$ $\displaystyle 8\pi$

Correct answer:

$16\pi$ $\displaystyle 16\pi$

Explanation:

Use the formula:

$\text{Area}=\pi\times r^2$ $\displaystyle \text{Area}=\pi\times r^2$

Where $\displaystyle r$ corresponds to the circle's radius.

Since r=4 $\displaystyle r=4$:

$\text{Area}=\pi\times(4^2)$ $\displaystyle \text{Area}=\pi\times(4^2)$

$\text{Area}=16\pi$ $\displaystyle \text{Area}=16\pi$

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Example Question #121 : Area

Find the area of a circle that has a radius of $\displaystyle x$.

Possible Answers:

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

$x\pi$ $\displaystyle x\pi$

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

$x^2\pi$ $\displaystyle x^2\pi$

Correct answer:

$x^2\pi$ $\displaystyle x^2\pi$

Explanation:

Use the formula:

$\text{Area}=\pi\times r^2$ $\displaystyle \text{Area}=\pi\times r^2$

Where $\displaystyle r$ corresponds to the circle's radius.

Since r=x $\displaystyle r=x$:

$\text{Area}=\pi\times(x^2)$ $\displaystyle \text{Area}=\pi\times(x^2)$

$\text{Area}=x^2\pi$ $\displaystyle \text{Area}=x^2\pi$

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Example Question #122 : Area

Find the area of a circle that has a radius of $\displaystyle 17$.

Possible Answers:

$17\pi$ $\displaystyle 17\pi$

$34\pi$ $\displaystyle 34\pi$

$128\pi$ $\displaystyle 128\pi$

$289\pi$ $\displaystyle 289\pi$

Correct answer:

$289\pi$ $\displaystyle 289\pi$

Explanation:

Use the formula:

$\text{Area}=\pi\times r^2$ $\displaystyle \text{Area}=\pi\times r^2$

Where $\displaystyle r$ corresponds to the circle's radius.

Since r=17 $\displaystyle r=17$:

$\text{Area}=\pi\times(17^2)$ $\displaystyle \text{Area}=\pi\times(17^2)$

$\text{Area}=289\pi$ $\displaystyle \text{Area}=289\pi$

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Example Question #123 : Area

Find the area of a circle with a diameter of $\displaystyle 12$.

Possible Answers:

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

$12\pi$ $\displaystyle 12\pi$

$24\pi$ $\displaystyle 24\pi$

$144\pi$ $\displaystyle 144\pi$

Correct answer:

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

Explanation:

Use the formula:

$\text{Area}=\pi\times r^2$ $\displaystyle \text{Area}=\pi\times r^2$

Where $\displaystyle r$ corresponds to the circle's radius.

We were given the circle's diameter, $\displaystyle d$.

d=2r $\displaystyle d=2r$

Substitute.

12=2r $\displaystyle 12=2r$

Divide both sides by $\displaystyle 2$.

$\frac{12}{2}=r$ $\displaystyle \frac{12}{2}=r$

r=6 $\displaystyle r=6$

Solve for the area of the circle.

$\text{Area}=\pi\times(6^2)$ $\displaystyle \text{Area}=\pi\times(6^2)$

$\text{Area}=36\pi$ $\displaystyle \text{Area}=36\pi$

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Pre-Algebra : Area

Study concepts, example questions & explanations for Pre-Algebra

All Pre-Algebra Resources

Example Questions

Example Question #3 : Area Of A Circle

Example Question #2 : Area Of A Circle

Example Question #4 : Area Of A Circle

Example Question #3 : Area Of A Circle

Example Question #5 : Area Of A Circle

Example Question #2 : Area Of A Circle

Example Question #122 : Area

Example Question #121 : Area

Example Question #122 : Area

Example Question #123 : Area

All Pre-Algebra Resources

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