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Pre-Algebra : Volume of a Rectangular Solid

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Example Questions

Example Question #251 : Geometry

Find the volume of a rectangular solid if the base area is and the height is .

Possible Answers:

576

Correct answer:

Explanation:

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

$V= LWH = A_{base}H$

The area of the base is length times width, and is already given. Multiply the area of the base with the height to obtain the volume.

$V=A_{base}H = 4(6)=24$

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Example Question #11 : Volume Of A Rectangular Solid

Find the volume of a rectangular box if the length, width, and height are $\textup{6, 15, and 11,}$ respectively.

Possible Answers:

897

909

495

330

990

Correct answer:

990

Explanation:

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

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

Substitute the dimensions.

V= (6)(15)(11)=990

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Example Question #12 : Volume Of A Rectangular Solid

Find the volume of the rectangular solid if the base has an area of and the height is .

Possible Answers:

Correct answer:

Explanation:

Write the formula for the volume of a rectangular solid.

$V=\textup{LWH}$

The base area is:

$\textup{B}_\textup{Area} = \textup{LW} = 4$

Substitute the area and the height.

$V=\textup{(LW)H} = 4(5)=20$

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Example Question #12 : Volume Of A Rectangular Solid

Find the volume of a rectangular solid with a length of 4, a width of 1, and a height of 10.

Possible Answers:

Correct answer:

Explanation:

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

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

Substitute the known dimensions.

$V=4 \times 1\times 10$

Multiply the numbers.

V=40

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Example Question #13 : Volume Of A Rectangular Solid

A matchbox has a length of 10 inches, width of 2 inches and height of 1 inch. What is the volume of the matchbox?

Possible Answers:

7in^2

20in^2

20 in^3

13in^3

13 in^2

Correct answer:

20 in^3

Explanation:

To find the volume of a rectangular solid you must multiply the length, width, and height together.

10 * 2 * 1 = 20in^3

Volume is in units cubed.

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Example Question #12 : Volume Of A Rectangular Solid

Alfred has a fish tank that looks like this:

Rectangle volumn

Alfred needs to fill the tank with water. To do that, he needs to know the volume of the tank. Find the volume of the tank if the height is 12 inches, the length is three times the height, and the width is the same as the height.

Possible Answers:

$432 \text{ inches}^3$

$5184 \text{ inches}^3$

$1296 \text{ inches}^3$

$432 \text{ inches}^2$

$5184 \text{ inches}^2$

Correct answer:

$5184 \text{ inches}^3$

Explanation:

The fish tankbis considered a rectangular prism. The formula to find the volume of a rectangular prism is

$V = l \cdot w \cdot h$

where l is the length, w is the width, and h is the height. We know the height is 12 inches. The length is three times the height, so the length is 36 inches. The width is the same as the height, sonthe width is 12 inches. Now, we can substitute. We get

$V = 36 \text{ inches} \cdot 12 \text{ inches} \cdot 12 \text{ inches}$

$V = 5184 \text{ inches}^3$

Therefore, the volume of the fish tank is $5184 \text{ inches}^3$ .

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Example Question #14 : Volume Of A Rectangular Solid

Find the volume of a rectangular box with the following dimensions:

Length: 4 feet. Width: 12 feet. Height: 3 feet.

Possible Answers:

19ft^3

36ft^3

144 ft^3

24ft^3

Correct answer:

144 ft^3

Explanation:

Find the volume of a rectangular box with the following dimensions:

Length: 4 feet. Width: 12 feet. Height: 3 feet.

To find volume of a rectangular box, we just need to use the following:

V=length*width*height

V=4ft*12ft*3ft=12ft*12ft^2=144ft^3

So our answer is:

144 ft^3

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Example Question #15 : Volume Of A Rectangular Solid

An aquarium is shaped like a perfect cube; the perimeter of each glass face is 8.4 meters. If it is filled to the recommended $90\%$ capacity, then, to the nearest hundred cubic liters, how much water will it contain?

Possible Answers:

$9\textup,300\textup{ L}$

$8\textup,300\textup{ L}$

$4\textup,000\textup{ L}$

Insufficient information is given to answer the question.

$4\textup,400\textup{ L}$

Note: $1\textup{ cubic meter}= 1\textup{,}000\textup{ cubic liters}$

Correct answer:

$8\textup,300\textup{ L}$

Explanation:

A perfect cube has square faces; if a face has perimeter 8.4 meters, then each side of each face measures one fourth of this, or 2.1 meters. The volume of the tank is the cube of this, or

$2.1^{3} = 9.261$ cubic meters.

Its capacity in liters is $9.261 \times 1,000 = 9,261$ liters.

$90\%$ of this is

$9,261 \times 0.9 = 8,335$ liters.

This rounds to $8\textup,300$ liters, the correct response.

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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 #251 : Geometry

Example Question #11 : Volume Of A Rectangular Solid

Example Question #12 : Volume Of A Rectangular Solid

Example Question #12 : Volume Of A Rectangular Solid

Example Question #13 : Volume Of A Rectangular Solid

Example Question #12 : Volume Of A Rectangular Solid

Example Question #14 : Volume Of A Rectangular Solid

Example Question #15 : Volume Of A Rectangular Solid

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