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Pre-Algebra : Area of a Circle

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Example Questions

Example Question #41 : Area Of A Circle

What is the area of a circle with a diameter of one unit?

Possible Answers:

$\frac{3}{2}\pi$

$\frac{1}{4}\pi$

$2\pi$

$\frac{1}{2}\pi$

$\pi$

Correct answer:

$\frac{1}{4}\pi$

Explanation:

Write the area of a circle.

$A=\pi r^2$

Since we are given the diameter of the circle and the area equation calls for the radius, we will need to calculate the radius first.

Divide the diameter by two to get the radius.

$r=\frac{D}{2}= \frac{1}{2}$

$A=\pi \left(\frac{1}{2}\right)^2 = \frac{1}{4}\pi$

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Example Question #41 : Area Of A Circle

Find the area of a circle with a circumference of .

Possible Answers:

$\frac{1}{4\pi}$

$\pi$

$\frac{1}{2\pi}$

$\frac{1}{4}$

$2\pi$

Correct answer:

$\frac{1}{4\pi}$

Explanation:

Write the circumference formula for the circle.

$C=2\pi r$

Substitute the circumference and solve for the radius.

$1=2\pi r$

$r=\frac{1}{2\pi}$

Write the formula for the area of the circle.

$A=\pi r^2$

Substitute the radius.

$A=\pi (\frac{1}{2\pi})^2 = \pi(\frac{1}{4\pi^2}) = \frac{1}{4\pi}$

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Example Question #42 : Area Of A Circle

Find the area of a circle with a diameter of 1.8 .

Possible Answers:

$3.24\pi$

$0.81 \pi$

$0.42\pi$

$1.62\pi$

$3.6\pi$

Correct answer:

$0.81 \pi$

Explanation:

Write the formula for the area of a circle.

$A=\pi r^2$

Given the diameter, we will need to divide this by two to obtain the radius.

$r=\frac{d}{2}= \frac{1.8}{2} = 0.9$

Substitute the radius and solve.

$A=\pi (0.9)^2 = 0.81 \pi$

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Example Question #41 : Area Of A Circle

Find the area of a circle with a radius of $\frac{2}{7}$ .

Possible Answers:

$\frac{\pi}{49}$

$\frac{4}{49}\pi$

$\frac{49}{4}$

$\frac{4}{7}\pi$

$\frac{4}{49}$

Correct answer:

$\frac{4}{49}\pi$

Explanation:

Write the formula for area of a circle.

$A=\pi r^2$

Substitute the radius.

$A=\pi (\frac{2}{7})^2 = \frac{4}{49}\pi$

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Example Question #44 : Area Of A Circle

Find the area of a circle with the diameter of $\frac{1}{10}$ .

Possible Answers:

$\frac{\pi}{25}$

$\frac{\pi}{200}$

$\frac{\pi}{400}$

$\frac{\pi}{50}$

$\frac{\pi}{100}$

Correct answer:

$\frac{\pi}{400}$

Explanation:

Write the formula to find the area of a circle.

$A=\pi r^2$

The radius is half the diameter.

$r=\frac{1}{2}d = \frac{1}{2} \times \frac{1}{10} = \frac{1}{20}$

Substitute the radius into the formula.

$A=\pi( \frac{1}{20})^2 = \frac{\pi}{400}$

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Example Question #45 : Area Of A Circle

The diameter of a circle is 21. Which of the following is the closest area?

Possible Answers:

1385

350

132

Correct answer:

350

Explanation:

Divide the diameter by two to obtain the radius.

$r=\frac{d}{2} = \frac{21}{2} = 10.5$

Write the area of a circle.

$A=\pi r^2$

Substitute the radius and solve. Assume $\pi = 3.14$ .

A=(3.14)(10.5)^2 = 346.185

The rounded answer is 350 .

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Example Question #46 : Area Of A Circle

Find the area of a circle with a circumference of $18\pi$ .

Possible Answers:

$162\pi$

$324\pi$

$81\pi$

$36\pi$

$9\pi$

Correct answer:

$81\pi$

Explanation:

Write the circumference formula and substitute the circumference.

$C=2\pi r$

$18\pi =2\pi r$

Now solve for r by dividing $2\pi$ on each side.

r=9

Write the formula to find the area of a circle.

$A=\pi r^2$

Since we solved for the radius in the above calculation, we will substitute that found value into the area formula and solve.

$A=\pi(9)^2 =81\pi$

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Example Question #47 : Area Of A Circle

Find the area of a circle with a diameter of 12.

Possible Answers:

$144\pi$

$36\pi$

144

$18\pi$

Correct answer:

$36\pi$

Explanation:

First identify the relationship between diameter and radius of a circle. Then, divide the diameter by two to get the radius.

$r=\frac{d}{2}= \frac{12}{2}=6$

Write the formula for the area of a circle.

$A=\pi r^2$

Substitute the radius.

$A=\pi (6)^2$

$A=36\pi$

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Example Question #162 : Area

Find the area of a circle with a diameter of $\pi$ .

Possible Answers:

$\frac{\pi^3}{4}$

$\frac{\pi^3}{2}$

$\frac{\pi^2}{2}$

$\pi^3$

Correct answer:

$\frac{\pi^3}{4}$

Explanation:

Write the formula for the area of a circle.

$A=\pi r^2$

To obtain the radius, divide the diameter by

$r=\frac{d}{2} = \frac{\pi}{2}$

Substitute the radius into the area.

$A=\pi \left (\frac{\pi}{2} \right )^2 = \frac{\pi^3}{4}$

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Example Question #163 : Area

Find the area of a circle in $\textup{feet}$ if the radius is $2 \textup{ inches}$ .

Possible Answers:

$\frac{\pi}{36}\textup{ feet}$

$4\pi\textup{ feet}$

$\frac{\pi}{12}\textup{ feet}$

$36\pi\textup{ feet}$

$\frac{\pi}{96}\textup{ feet}$

Correct answer:

$\frac{\pi}{36}\textup{ feet}$

Explanation:

Convert $\textup{2 inches}$ to $\textup{feet}$ . There are $\textup{12 inches}$ in a foot.

$r= 2 \textup{ inches }(\frac{1 \textup{ foot}}{12 \textup{ inches }}) = \frac{1}{6} \textup{ foot}$

Write the formula for area of a circle and substitute the new radius.

$A=\pi r^2 = \pi (\frac{1}{6})^2 =\frac{\pi}{36}\textup{ feet}$

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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 #41 : Area Of A Circle

Example Question #41 : Area Of A Circle

Example Question #42 : Area Of A Circle

Example Question #41 : Area Of A Circle

Example Question #44 : Area Of A Circle

Example Question #45 : Area Of A Circle

Example Question #46 : Area Of A Circle

Example Question #47 : Area Of A Circle

Example Question #162 : Area

Example Question #163 : Area

All Pre-Algebra Resources

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