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Pre-Algebra : Area of a Circle

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Example Questions

Example Question #11 : Area Of A Circle

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

Possible Answers:

$4x\pi$

$x^2\pi$

$2x\pi$

$x\pi$

Correct answer:

$x^2\pi$

Explanation:

Use the formula:

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

Where corresponds to the circle's radius.

Since r=x :

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

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

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Example Question #12 : Area Of A Circle

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

Possible Answers:

$34\pi$

$289\pi$

$128\pi$

$17\pi$

Correct answer:

$289\pi$

Explanation:

Use the formula:

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

Where corresponds to the circle's radius.

Since r=17 :

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

$\text{Area}=289\pi$

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Example Question #11 : Area Of A Circle

Find the area of a circle with a diameter of .

Possible Answers:

$24\pi$

$36\pi$

$144\pi$

$12\pi$

Correct answer:

$36\pi$

Explanation:

Use the formula:

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

Where corresponds to the circle's radius.

We were given the circle's diameter, .

d=2r

Substitute.

12=2r

Divide both sides by .

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

r=6

Solve for the area of the circle.

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

$\text{Area}=36\pi$

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Example Question #11 : Area Of A Circle

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

Possible Answers:

$48\pi$

$24\pi$

$144\pi$

$36\pi$

Correct answer:

$144\pi$

Explanation:

Use the formula:

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

Where corresponds to the circle's radius.

We were given the circle's diameter, .

d=2r

Substitute.

24=2r

Divide both sides by .

$\frac{24}{2}=r$

r=12

Solve for the area of the circle.

$\text{Area}=\pi\times(12^2)$

$\text{Area}=144\pi$

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Example Question #131 : Geometry

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

Possible Answers:

$36\pi$

$324\pi$

$68\pi$

$81\pi$

Correct answer:

$81\pi$

Explanation:

Use the formula:

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

Where corresponds to the circle's radius.

We were given the circle's diameter, .

d=2r

Substitute.

18=2r

Divide both sides by .

$\frac{18}{2}=r$

r=9

Solve for the area of the circle.

$\text{Area}=\pi\times(9^2)$

$\text{Area}=81\pi$

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Example Question #132 : Geometry

Find the area of a circle that has a circumference of $16\pi$

Possible Answers:

$64\pi$

$196\pi$

$36\pi$

$16\pi$

Correct answer:

$64\pi$

Explanation:

Use the formula:

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

Where corresponds to the circle's radius.

We were given the circle's circumference, .

$C=\pi\times d$

Solve for to find the circle's diameter.

$16\pi=\pi\times d$

Divide both sides by $\pi$ .

$\frac{16\pi}{\pi}=d$

d=16

Now we have the circle's diameter, . We can find the radius, .

d=2r

Substitute.

16=2r

Divide both sides by .

$\frac{16}{2}=r$

r=8

Solve for the area of the circle.

$\text{Area}=\pi\times(8^2)$

$\text{Area}=64\pi$

Report an Error

Example Question #14 : Area Of A Circle

Find the area of a circle that has a circumference of $10\pi$ .

Possible Answers:

$5\pi$

$50\pi$

$100\pi$

$25\pi$

Correct answer:

$25\pi$

Explanation:

Use the formula:

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

Where corresponds to the circle's radius.

We were given the circle's circumference, .

$C=\pi\times d$

Solve for to find the circle's diameter.

$10\pi=\pi\times d$

Divide both sides by $\pi$ .

$\frac{10\pi}{\pi}=d$

d=10

Now we have the circle's diameter, . We can find the radius, .

d=2r

Substitute.

10=2r

Divide both sides by .

$\frac{10}{2}=r$

r=5

Solve for the area of the circle.

$\text{Area}=\pi\times(5^2)$

$\text{Area}=25\pi$

Report an Error

Example Question #15 : Area Of A Circle

Find the area of a circle that has a circumference of $26\pi$ .

Possible Answers:

$169\pi$

$26\pi$

$676\pi$

$104\pi$

Correct answer:

$169\pi$

Explanation:

Use the formula:

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

Where corresponds to the circle's radius.

We were given the circle's circumference, .

$C=\pi\times d$

Solve for to find the circle's diameter.

$26\pi=\pi\times d$

Divide both sides by $\pi$ .

$\frac{26\pi}{\pi}=d$

d=26

Now we have the circle's diameter, . We can find the radius, .

d=2r

Substitute.

26=2r

Divide both sides by .

$\frac{26}{2}=r$

r=13

Solve for the area of the circle.

$\text{Area}=\pi\times(13^2)$

$\text{Area}=169\pi$

Report an Error

Example Question #13 : Area Of A Circle

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

Possible Answers:

$\frac{4x^{2}}{\pi}$

$8x\pi$

$16x^2\pi$

$2x^2\pi$

Correct answer:

$\frac{4x^{2}}{\pi}$

Explanation:

Use the formula:

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

Where corresponds to the circle's radius.

We were given the circle's circumference, .

$C=\pi\times d$

Solve for to find the circle's diameter.

$4x=\pi\times d$

Divide both sides by $\pi$ .

$\frac{4x}{\pi}=d$

$d=\frac{4x}{\pi}$

Now we have the circle's diameter, . We can find the radius, .

d=2r

Substitute.

$\frac{4x}{\pi}=2r$

Divide both sides by .

$\frac{4x}{2\pi}=r$

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

Solve for the area of the circle.

$\text{Area}=\pi\times\left ( \frac{2x}{\pi} \right )^{2}$

$\text{Area}=\pi\times\left ( \frac{4x^{2}}{\pi^{2}} \right )$

Simplify.

$\text{Area}= \frac{4x^{2}}{\pi}$

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Example Question #17 : Area Of A Circle

Find the area of a circle that has a circumference of $20\pi$ .

Possible Answers:

$40\pi$

$400\pi$

$100\pi$

$125\pi$

Correct answer:

$100\pi$

Explanation:

Use the formula:

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

Where corresponds to the circle's radius.

We were given the circle's circumference, .

$C=\pi\times d$

Solve for to find the circle's diameter.

$20\pi=\pi\times d$

Divide both sides by $\pi$ .

$\frac{20\pi}{\pi}=d$

d=20

Now we have the circle's diameter, . We can find the radius, .

d=2r

Substitute.

20=2r

Divide both sides by .

$\frac{20}{2}=r$

r=10

Solve for the area of the circle.

$\text{Area}=\pi\times(10^2)$

$\text{Area}=100\pi$

Report an Error

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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 #11 : Area Of A Circle

Example Question #12 : Area Of A Circle

Example Question #11 : Area Of A Circle

Example Question #11 : Area Of A Circle

Example Question #131 : Geometry

Example Question #132 : Geometry

Example Question #14 : Area Of A Circle

Example Question #15 : Area Of A Circle

Example Question #13 : Area Of A Circle

Example Question #17 : Area Of A Circle

All Pre-Algebra Resources

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