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Pre-Algebra : Area of a Circle

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Example Questions

Example Question #1 : Area Of A Circle

A circle has a circumference of $\small 6\pi$ . What is its area?

Possible Answers:

$\small 18\pi$

$\small 9\pi$

$\small 12\pi$

$\small 6\pi$

$\small 36\pi$

Correct answer:

$\small 9\pi$

Explanation:

To begin, we need to find the radius of the circle. The circumference of a circle is given as follows:

$\small C = 2\pi r$ ,

where is the radius.

Then, a circle with circumference $6\pi$ will have the following radius:

$6\pi = 2\pi r$

$\small \frac{6\pi}{2\pi}=\frac{2\pi r}{2\pi}$

$\small 3=r$

Using the radius, we can now solve for the area:

$\small A=\pi r^2$

$A=\pi(3)^2$

$\small A=9\pi$

The area of the circle is $\small 9\pi$ .

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Example Question #2 : Area Of A Circle

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

Possible Answers:

$12.25\pi$

$49\pi$

$24.5\pi$

$98\pi$

Correct answer:

$12.25\pi$

Explanation:

If the diameter is 7, then the radius is half of 7, or 3.5.

Plug this value for the radius into the equation for the area of a circle:

$A=r^2\pi=(3.5)^2\pi=12.25\pi$

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Example Question #3 : Area Of A Circle

Untitled_1

The rectangle in the above figure has length 20 and height 10. What is the area of the orange region?

Possible Answers:

$200 + \frac{25}{2} \pi$

$200 + 100 \pi$

$200 + 50 \pi$

Insufficient information is given to determine the area.

$200 + 25 \pi$

Correct answer:

$200 + \frac{25}{2} \pi$

Explanation:

The orange region is a composite of two figures:

One is a rectangle measuring 20 by 10, which, subsequently, has area

$20 \cdot 10 = 200$ .

The other is a semicircle with diameter 10, and, subsequently, radius 5. Its area is

$\frac{1}{2} \pi \cdot 5^{2} = \frac{25}{2} \pi$ .

Add the areas:

$A = 200 + \frac{25}{2} \pi$

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Example Question #3 : Area Of A Circle

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

Possible Answers:

$75.4 \textup{ in}^2$

$56.7 \textup{ in}^2$

$78.5 \textup{ in}^2$

$314.3 \textup{ in}^2$

$45.8 \textup{ in}^2$

Correct answer:

$78.5 \textup{ in}^2$

Explanation:

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

First you must find the radius from the diameter.

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

In this case it is,

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

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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 : 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 #3 : Area Of A Circle

Find the area of a circle that has a radius of .

Possible Answers:

$4\pi$

$8\pi$

$12\pi$

$16\pi$

Correct answer:

$16\pi$

Explanation:

Use the formula:

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

Where corresponds to the circle's radius.

Since r=4 :

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

$\text{Area}=16\pi$

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Pre-Algebra : Area of a Circle

Study concepts, example questions & explanations for Pre-Algebra

All Pre-Algebra Resources

Example Questions

Example Question #1 : Area Of A Circle

Example Question #2 : Area Of A Circle

Example Question #3 : Area Of A Circle

Example Question #3 : Area Of A Circle

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 : Area Of A Circle

Example Question #3 : Area Of A Circle

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