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Pre-Algebra : Volume of a Rectangular Solid

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Example Questions

Example Question #243 : Geometry

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:

$24in.^{3}$

$512in.^{3}$

$48in.^{3}$

$768in.^{3}$

$384in.^{3}$

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 #1 : Volume Of A Rectangular Solid

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

Possible Answers:

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

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

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

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

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 #245 : Geometry

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 x 10^-3

3.2

3,2 x 10³

3.2 x 10⁶

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 : Finding Volume Of A Cube

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

Possible Answers:

512

500

Not enough information provided.

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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Example Question #1 : Finding Volume Of A Cube

What is the volume of a cube with a side length equal to inches?

Possible Answers:

$53\: in^{3}$

$343\: in^{3}$

$21\: in^{3}$

$49\: in^{3}$

Correct answer:

$343\: in^{3}$

Explanation:

The volume of a a cube (or rectangular prism) can be solved using the following equation:

$V=l\times\ w\times\ h$

$V=7in\times 7in\times 7in=343in^3$

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Example Question #2 : Volume Of A Rectangular Solid

The volume of a cube is . What is the length of an edge of the cube?

Possible Answers:

Correct answer:

Explanation:

Let be the length of an edge of the cube. The volume of a cube can be determined by the equation:
x^3=V

x^3=64

$\sqrt[3]{x^3}=\sqrt[3]{64}$

x=4

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Example Question #5 : Volume Of A Rectangular Solid

A given rectangular prism has a length of $9\:cm$ , a width of $5\:cm$ , and a height of $7\:cm$ . What is the volume of the prism?

Possible Answers:

$315\:cm^{3}$

$63\:cm^{2}$

$315\:cm^{2}$

$45\:cm^{3}$

$63\:cm^{3}$

Correct answer:

$315\:cm^{3}$

Explanation:

The volume of a given prism V=Bh , where is the base area and is the height. For a rectangular prism, the base area $B=l \times w$ , or length times width. Therefore:

V=Bh

$V=(l\times w)h$

Substituting in our known values:

$V=(9\:cm\times 5\:cm)7\:cm$

$V=45\:cm^{2}\times 7\:cm$

$V=315\:cm^{3}$

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Example Question #3 : Volume Of A Rectangular Solid

A given rectangular prism has a length of , a width of , and a height of . What is the volume of the prism?

Possible Answers:

574

572

576

Correct answer:

576

Explanation:

The volume of a rectangular prism is the product of its base area and its height : V=Ah . Since we can determine the base area of the rectangular prism from its length and width, we can rewrite the equation and solve:

V=Ah

V=lwh

V=(12)(6)(8)

$V=12 \times48$

V=576

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Example Question #3 : Volume Of A Rectangular Solid

A given rectangular prism has a length of 10cm , a width of 7cm , and a height of 15cm , what is its volume?

Possible Answers:

$525cm^{3}$

$1050cm^{2}$

$85cm^{3}$

$1050cm^{3}$

$32cm^{3}$

Correct answer:

$1050cm^{3}$

Explanation:

V=Ah

V=lwh

V=(10)(7)(25)

V=1050

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Example Question #4 : Volume Of A Rectangular Solid

The length, width, and height of box is 2,5,9 respectively. What is the volume of the rectangular box?

Possible Answers:

Correct answer:

Explanation:

Write the formula to find the volume of a rectangular solid.

$V=\textup{ Length} \times \textup{Width} \times\textup{ Height}$

Substitute the dimensions.

$2\times5\times9 = 90$

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Pre-Algebra : Volume of a Rectangular Solid

Study concepts, example questions & explanations for Pre-Algebra

All Pre-Algebra Resources

Example Questions

Example Question #243 : Geometry

Example Question #1 : Volume Of A Rectangular Solid

Example Question #245 : Geometry

Example Question #1 : Finding Volume Of A Cube

Example Question #1 : Finding Volume Of A Cube

Example Question #2 : Volume Of A Rectangular Solid

Example Question #5 : Volume Of A Rectangular Solid

Example Question #3 : Volume Of A Rectangular Solid

Example Question #3 : Volume Of A Rectangular Solid

Example Question #4 : Volume Of A Rectangular Solid

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