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Pre-Algebra : Geometry

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Example Questions

Example Question #11 : Volume Of A Cylinder

Solve for the volume of a cylinder if the radius is and the height is twice the radius.

Possible Answers:

$432\pi$

$441\pi$

$686 \pi$

$196\pi$

$1372\pi$

Correct answer:

$686 \pi$

Explanation:

Write the formula for the volume of the cylinder.

$V=\pi r^2 h$

The height is 14, since it is twice the radius. Substitute the dimensions.

$\\V=\pi (7)^2 (14 ) \\V=\pi 49\cdot 14\\ V=686 \pi$

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Example Question #52 : Volume

Solve for the volume of a cylindrical soda can if the base perimeter is $6\pi$ and the height is .

Possible Answers:

$54\pi$

$27\pi$

$18\pi$

$108\pi$

$36\pi$

Correct answer:

$54\pi$

Explanation:

Write the formula for the volume of a cylinder.

$V=\pi r^2h$

The radius is unknown. In order to solve for the radius, use the base perimeter as a given to solve for the radius. The base perimeter is the circular circumference.

Write the formula for the circle's circumference.

$C=2\pi r$

Substitute the base perimeter.

$6\pi=2\pi r$

Divide $2\pi$ on both sides to solve for the radius.

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

r=3

Substitute the radius and the height into the volume formula.

$V=\pi r^2h = \pi (3)^2 (6) = \pi (9)(6) =54\pi$

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Example Question #53 : Volume

You have a can of soup that looks like the following.

Volume2

The height is 5 in and the diameter is 4 in. If $\pi = 3.14$ , find the volume of the soup can. Round to the nearest tenths.

Possible Answers:

251.2in^2

125.6in^3

251.2in^3

62.8in^3

62.8in^2

Correct answer:

62.8in^3

Explanation:

The formula to find the volume of a cylinder is

$V = \pi r^2 h$

We know the diameter of the cylinder is 4in. The radius is half the diameter, so the radius of the cylinder is 2in. We know,

$\pi = 3.14$

$r = 2\text{in}$

$h = 5 \text{in}$

When we substitute into the formula, we get

$V = 3.14 * (2\text{in})^2 * 5\text{in}$

$V = 3.14 * 4\text{in}^2 * 5\text{in}$

$V = 62.8\text{in}^3$

Therefore, the volume of the soup can is $62.8\text{in}^3$

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Example Question #54 : Volume

A cylinder has a volume of $288\pi$ . If the height of the cylinder is , what is the radius?

Possible Answers:

Correct answer:

Explanation:

The formula for the volume of a cylinder is:

$V=\pi r^2h$

To find the radius, we simply plug in the given values and solve for :

$288\pi =\pi r^2(8)$

$\frac{288\pi}{\pi} =\frac{8\pi r^2}{\pi}$

288=8r^2

$\frac{288}{8}=\frac{8r^2}{8}$

36=r^2

$\sqrt{36}=\sqrt{r^2}$

6=r

Therefore, the radius of the circle is .

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Example Question #55 : Volume

If Cindy has a cylindrical bucket filled with sand, how much sand does it contain if area of the circular bottom is $10\pi$ inches and the heigh of the bucket is inches?

Possible Answers:

$80\ in^3$

$40\pi\ in^3$

$800\pi\ in^3$

$80\pi\ in^3$

Correct answer:

$80\pi\ in^3$

Explanation:

To find the volume of a cylinder, the formula is $V = \pi r^{2} h$ .
Normally, you would simply input the radius given for "" and the height given for "". However, the question did not directly give us the radius; it gave us the area of the circular bottom.

Now examine the volume formula closely, and you will see that the formula for the area of a circle is hidden inside the volume formula. If $\pi r^{2}$ is the area of a circle, then we can simply multiply the area of the circle given by the height given.

V = area of the circle x height
$V=10\pi \times 8$
$V=80\pi$ cubed inches

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Example Question #12 : Volume Of A Cylinder

Find the volume of the cylinder if the base has a circumference of $4\pi$ and the height is 4.

Possible Answers:

$16\pi$

$32\pi$

$4\pi$

$8\pi$

Correct answer:

$16\pi$

Explanation:

The base of a cylinder is a circle. Write the circumference formula.

$C=2\pi r$

Substitute the circumference and find the radius.

$4\pi=2\pi r$

r=2

Write the formula to find the volume for cylinders.

$V=\pi r^2h$

Substitute the dimensions.

$V=\pi (2)^2 (4) = 16\pi$

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Example Question #1 : Volume Of A Rectangular Solid

Trayvon ordered a new calculator online for his Pre-Algebra class. When it arrived in the mail, he noticed something interesting about the rectangular box it was shipped in. The width of the box was twice the height, and the length of the box was three times the width. If the box was four inches tall, what was the volume of the box?

Possible Answers:

$48in.^{3}$

$512in.^{3}$

$768in.^{3}$

$384in.^{3}$

$24in.^{3}$

Correct answer:

$768in.^{3}$

Explanation:

If the box is 4 inches tall, then its height is 4in. Since the width is twice the height, the width must be 8 inches. Since the length is three times the width, the length must be 24 inches. Since a rectangular box is just a rectangular solid, the formula for the volume of a rectangular solid will give us the volume of the Trayvon's box.

V=lwh , where is length, is width, and is height. Therefore,

V=(24)(8)(4)=768

Since the unit of each of our dimensions was inches, our volume will be in cubic inches. Thus our answer is $768in.^{3}$

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Example Question #2 : How To Find The Volume Of A Net

A rectangular prism has length 24 inches, width 18 inches, and height 15 inches. Give its volume in cubic feet.

Possible Answers:

$4 \frac{3}{4} \textrm{ ft}^{3}$

$4 \frac{1}{2} \textrm{ ft}^{3}$

$4 \frac{1}{4} \textrm{ ft}^{3}$

$3 \frac{3}{4} \textrm{ ft}^{3}$

Correct answer:

$3 \frac{3}{4} \textrm{ ft}^{3}$

Explanation:

Divide each dimension in inches by 12 to convert from inches to feet:

$L = 24 \div 12 = 2$ feet

$W = 18 \div 12 = 1 \frac{1}{2} = \frac{3}{2}$ feet

$H = 15 \div 12 = 1 \frac{1}{4} = \frac{5}{4}$ feet

Multiply the three to get the volume:

$V = LWH = 2 \cdot \frac{3}{2} \cdot \frac{5}{4} = \frac{15}{4} = 3 \frac{3}{4}$ cubic feet

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Example Question #1 : Volume Of A Rectangular Solid

A rectangular box has a length of 2 meters, a width of 0.5 meters, and a height of 3.2 meters. How many cubes with a volume of one cubic centimeter could fit into this rectangular box?

Possible Answers:

3.2 x 10²

3.2

3.2 x 10^-3

3.2 x 10⁶

3,2 x 10³

Correct answer:

3.2 x 10⁶

Explanation:

In order to figure out how many cubic centimeters can fit into the box, we need to figure out the volume of the box in terms of cubic centimeters. However, the measurements of the box are given in meters. Therefore, we need to convert these measurements to centimeters and then determine the volume of the box.

There are 100 centimeters in one meter. This means that in order to convert from meters to centimeters, we must multiply by 100.

The length of the box is 2 meters, which is equal to 2 x 100, or 200, centimeters.

The width of the box is 0.5(100) = 50 centimeters.

The height of the box is 3.2(100) = 320 centimeters.

Now that all of our measurements are in centimeters, we can calculate the volume of the box in cubic centimeters. Remember that the volume of a rectangular box (or prism) is equal to the product of the length, width, and height.

V = length x width x height

V = (200 cm)(50 cm)(320 cm) = 3,200,000 cm³

To rewrite this in scientific notation, we must move the decimal six places to the left.

V = 3.2 x 10⁶ cm³

The answer is 3.2 x 10⁶.

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Example Question #1 : Volume Of A Rectangular Solid

If a cube is inches tall, what is its volume?

Possible Answers:

Not enough information provided.

500

512

384

Correct answer:

512

Explanation:

To find the volume of a cube, we multiply length by width by height, which can be represented with the forumla $v=l\cdot w\cdot h$ . Since a cube has equal sides, we can use for all three values.

$8\cdot 8\cdot 8=512\: in ^{3}$

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Pre-Algebra : Geometry

Study concepts, example questions & explanations for Pre-Algebra

All Pre-Algebra Resources

Example Questions

Example Question #11 : Volume Of A Cylinder

Example Question #52 : Volume

Example Question #53 : Volume

Example Question #54 : Volume

Example Question #55 : Volume

Example Question #12 : Volume Of A Cylinder

Example Question #1 : Volume Of A Rectangular Solid

Example Question #2 : How To Find The Volume Of A Net

Example Question #1 : Volume Of A Rectangular Solid

Example Question #1 : Volume Of A Rectangular Solid

All Pre-Algebra Resources

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