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Pre-Algebra : Area

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Example Questions

Example Question #131 : Area

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

Possible Answers:

$48\pi$

$36\pi$

$144\pi$

$24\pi$

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 #132 : Area

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

Possible Answers:

$81\pi$

$68\pi$

$324\pi$

$36\pi$

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 #133 : Area

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

Possible Answers:

$36\pi$

$196\pi$

$16\pi$

$64\pi$

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.

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

$\text{Area}=64\pi$

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Example Question #134 : Area

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

Possible Answers:

$5\pi$

$100\pi$

$25\pi$

$50\pi$

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.

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

$\text{Area}=25\pi$

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Example Question #135 : Area

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

Possible Answers:

$26\pi$

$169\pi$

$104\pi$

$676\pi$

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 #136 : Area

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

Possible Answers:

$8x\pi$

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

$16x^2\pi$

$2x^2\pi$

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 #137 : Area

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

Possible Answers:

$100\pi$

$40\pi$

$125\pi$

$400\pi$

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

Example Question #138 : Area

Find the area of a circle that has a circumference of $22\pi$ .

Possible Answers:

$224\pi$

$121\pi$

$22\pi$

$484\pi$

Correct answer:

$121\pi$

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.

$22\pi=\pi\times d$

Divide both sides by $\pi$ .

$\frac{22\pi}{\pi}=d$

d=22

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

d=2r

Substitute.

22=2r

Divide both sides by .

$\frac{22}{2}=r$

r=11

Solve for the area of the circle.

$\text{Area}=\pi\times(11^2)$

$\text{Area}=121\pi$

Report an Error

Example Question #139 : Area

Find the area of the circle inscribed inside a square with sides that measure 4 ft. Halfcircle3

Possible Answers:

$8\pi \textup{ ft}^{2}$

$4\pi \textup{ ft}^{2}$

$4\sqrt{2}\pi \textup{ ft}^{2}$

$2\pi \textup{ ft}^{2}$

$16\pi \textup{ ft}^{2}$

Correct answer:

$4\pi \textup{ ft}^{2}$

Explanation:

The area of a circle is $A=\pi r^{2}$

When a circle is inscribed in a square, the diameter of the circle is equal to the length of each side of the square. Since we know the diameter is 4ft. long, we know that the radius is 2 ft. long. Now substitute r into the equation for the area of a circle.

$A=\pi (2\, ft.)^{2}=4\pi \,ft.^{2}$

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Example Question #140 : Area

A cylindrical piece of steel that is 12 inches long tapers at either end into circles of different diameter. One end is 3 inches in diameter and the other is 4 inches in diameter. What is the total surface area of the ends of this steel bar?

Possible Answers:

89.5in^2

12.6in^2

19.7in^2

29.3in^2

None of the other answers.

Correct answer:

19.7in^2

Explanation:

To find the area of a circle use the formula $\pi r^2$ . After finding the area for both circles, add them for the total surface area of the ends of the steel bar.

Circle (4in diameter): $\pi r^2=\pi 2^2=12.6in^2$

Circle (3in diameter): $\pi r^2=\pi 1.5^2=7.1in^2$

Total area: 12.6in^2+7.1in^2=19.7in^2

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Pre-Algebra : Area

Study concepts, example questions & explanations for Pre-Algebra

All Pre-Algebra Resources

Example Questions

Example Question #131 : Area

Example Question #132 : Area

Example Question #133 : Area

Example Question #134 : Area

Example Question #135 : Area

Example Question #136 : Area

Example Question #137 : Area

Example Question #138 : Area

Example Question #139 : Area

Example Question #140 : Area

All Pre-Algebra Resources

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