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Pre-Algebra : Area of a Circle

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Example Questions

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.

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

$\text{Area}=121\pi$

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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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Example Question #21 : Area Of A Circle

Units = cm

Diameter is 30, find the area of the circle.

Possible Answers:

$\small 12.5cm{2}$

$\small 392cm^{2}$

$\small 706$

$\small \small 706.5cm^{2}$

Correct answer:

$\small \small 706.5cm^{2}$

Explanation:

To find the area of a circle we use the equation:

$A=\small \pi(r)^{2}$ .

In this question we are told that the diameter of the circle, meaning the radius is half of this.

To solve for the area, we just plug it into our equation:

$r=\frac{1}{2}d\rightarrow r=\frac{1}{2}30=15$

$\\A=\small \small \small \small \small \small \pi(15)^{2}\\A = 15\times15\times \pi \\A= 225\pi \\A= 225\times 3.14 \\A= 706.5cm$ .

And because we are working with the area of a shape, our answer must have units that are squared, therefore: $\small \small \small \small 706.5cm^{2}$ .

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Example Question #22 : Area Of A Circle

Units = cm

Radius is five, find the area of the circle.

Possible Answers:

$\small 78.5cm^{2}$

$\small 74cm^{2}$

$\small 238.5cm^{2}$

$\small 58.5cm^{3}$

Correct answer:

$\small 78.5cm^{2}$

Explanation:

To find the area of a circle we use the equation:

$A=\small \pi(r)^{2}$ .

In this question we are told that the radius of the circle is five. To solve for the area, we just plug it into our equation:

$\\ A=\small \small \small \pi(5)^{2} \\ A= 5\times5 \times \pi \\A= 25\pi \\A= 25 \times 3.14 \\A= 78.5cm$ .

And because we are working with the area of a shape, our answer must have units that are squared, therefore: $\small 78.5cm^{2}$ .

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Example Question #23 : Area Of A Circle

Units = cm

Radius is $\small 6.5$ , find the area of the circle.

Possible Answers:

$\small 142.25cm^{2}$

$132.665cm^{2}$

$\small 12.665cm^{2}$

$\small 100cm^{2}$

Correct answer:

$132.665cm^{2}$

Explanation:

To find the area of a circle we use the equation:

$A=\small \pi(r)^{2}$ .

In this question we are told that the radius of the circle is 6.5.

To solve for the area, we just plug it into our equation:

$\\A=\small \small \small \small \pi(6.5)^{2} \\A= 6.5\times6.5 \times \pi \\A= 42.45\pi \\A= 42.25 \times 3.14\\A = 132.665cm$ .

And because we are working with the area of a shape, our answer must have units that are squared, therefore: $\small \small 132.665cm^{2}$ .

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Example Question #24 : Area Of A Circle

Units = cm

Radius is four, find the area of the circle.

Possible Answers:

$\small 40.24cm^{2}$

$10.24cm^{2}$

$\small 50.24cm^{2}$

$\small 45cm^{2}$

Correct answer:

$\small 50.24cm^{2}$

Explanation:

To find the area of a circle we use the equation:

$A=\small \pi(r)^{2}$ .

In this question we are told that the radius of the circle is four. To solve for the area, we just plug it into our equation:

$\\A=\small \small \small \small \small \pi(4)^{2}\\A = 4\times4 \times \pi \\A=16\pi \\A= 16 \times 3.14 \\A= 50.24cm$ .

And because we are working with the area of a shape, our answer must have units that are squared, therefore: $\small \small \small 50.24cm^{2}$ .

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Example Question #25 : Area Of A Circle

Units = cm

Radius is two, find the area of the circle.

Possible Answers:

$\small 11cm^{2}$

$\small 15cm^{2}$

$\small 2.56cm^{2}$

$\small 12.56cm^{2}$

Correct answer:

$\small 12.56cm^{2}$

Explanation:

To find the area of a circle we use the equation:

$A=\small \pi(r)^{2}$ .

In this question we are told that the radius of the circle is two.

To solve for the area, we just plug it into our equation:

$\\ A=\small \small \small \small \small \small \pi(2)^{2} \\A= 2\times2\times \pi \\A=4\pi \\A=4 \times 3.14 \\A= 12.56cm$ .

And because we are working with the area of a shape, our answer must have units that are squared, therefore: $\small \small \small \small 12.56cm^{2}$ .

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Example Question #26 : Area Of A Circle

Units = cm

Radius is ten, find the area of the circle.

Possible Answers:

$\small 31.4cm^{2}$

$\small .314cm^{2}$

$\small 314cm^{2}$

$\small 31400cm^{2}$

Correct answer:

$\small 314cm^{2}$

Explanation:

To find the area of a circle we use the equation:

$A=\small \pi(r)^{2}$ .

In this question we are told that the radius of the circle is ten.

To solve for the area, we just plug it into our equation:

$\\A=\small \small \small \small \small \small \small \pi(10)^{2} \\A= 10\times10\times \pi \\A=100\pi \\A=4 \times 3.14 \\A= 314cm$ .

And because we are working with the area of a shape, our answer must have units that are squared, therefore: $\small \small \small \small \small 314cm^{2}$ .

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Example Question #27 : Area Of A Circle

Units = cm

Diameter is 16, find the area of the circle.

Possible Answers:

$\small 32.6cm^{2}$

$\small 200.96cm^{2}$

$\small 20.96cm^{2}$

$\small 56cm^{2}$

Correct answer:

$\small 200.96cm^{2}$

Explanation:

To find the area of a circle we use the equation:

$A=\small \pi(r)^{2}$ .

In this question we are told that the diameter of the circle, meaning the radius is half of this. To solve for the area, we just plug it into our equation:

$r=\frac{1}{2}d\rightarrow r=\frac{1}{2}16=8$

$\\A=\small \small \small \small \pi(8)^{2} = 8\times8\times \pi \\A= 64\pi \\A= 64 \times 3.14 \\A= 200.96cm$ .

And because we are working with the area of a shape, our answer must have units that are squared, therefore: $\small \small200.96cm^{2}$ .

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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 #138 : Area

Example Question #139 : Area

Example Question #140 : Area

Example Question #21 : Area Of A Circle

Example Question #22 : Area Of A Circle

Example Question #23 : Area Of A Circle

Example Question #24 : Area Of A Circle

Example Question #25 : Area Of A Circle

Example Question #26 : Area Of A Circle

Example Question #27 : Area Of A Circle

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