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Pre-Algebra : Volume of a Rectangular Solid

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Example Questions

Example Question #61 : Volume

Find the volume of a rectangular solid if the base area is $\displaystyle 4$ and the height is $\displaystyle 6$.

Possible Answers:

$\displaystyle 12$

$\displaystyle 24$

$\displaystyle 22$

576 $\displaystyle 576$

$\displaystyle 96$

Correct answer:

$\displaystyle 24$

Explanation:

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

$V= LWH = A_{base}H$ $\displaystyle V= LWH = A_{base}H$

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.

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

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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 $\textup{6, 15, and 11,}$ $\displaystyle \textup{6, 15, and 11,}$ respectively.

Possible Answers:

897 $\displaystyle 897$

909 $\displaystyle 909$

495 $\displaystyle 495$

330 $\displaystyle 330$

990 $\displaystyle 990$

Correct answer:

990 $\displaystyle 990$

Explanation:

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

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

Substitute the dimensions.

$\displaystyle V= (6)(15)(11)=990$

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Example Question #62 : Volume

Find the volume of the rectangular solid if the base has an area of $\displaystyle 4$ and the height is $\displaystyle 5$.

Possible Answers:

$\displaystyle 20$

$\displaystyle 40$

$\displaystyle 80$

$\displaystyle 15$

$\displaystyle 50$

Correct answer:

$\displaystyle 20$

Explanation:

Write the formula for the volume of a rectangular solid.

$V=\textup{LWH}$ $\displaystyle V=\textup{LWH}$

The base area is:

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

Substitute the area and the height.

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

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Example Question #14 : 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:

$\displaystyle 15$

$\displaystyle 40$

$\displaystyle 41$

$\displaystyle 20$

$\displaystyle 21$

Correct answer:

$\displaystyle 40$

Explanation:

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

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

Substitute the known dimensions.

$V=4 \times 1\times 10$ $\displaystyle V=4 \times 1\times 10$

Multiply the numbers.

V=40 $\displaystyle V=40$

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Example Question #12 : 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:

13 in^2 $\displaystyle 13 in^2$

7in^2 $\displaystyle 7in^2$

20in^2 $\displaystyle 20in^2$

20 in^3 $\displaystyle 20 in^3$

13in^3 $\displaystyle 13in^3$

Correct answer:

20 in^3 $\displaystyle 20 in^3$

Explanation:

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

$\displaystyle 10 * 2 * 1 = 20in^3$

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:

$432 \text{ inches}^3$ $\displaystyle 432 \text{ inches}^3$

$5184 \text{ inches}^3$ $\displaystyle 5184 \text{ inches}^3$

$1296 \text{ inches}^3$ $\displaystyle 1296 \text{ inches}^3$

$432 \text{ inches}^2$ $\displaystyle 432 \text{ inches}^2$

$5184 \text{ inches}^2$ $\displaystyle 5184 \text{ inches}^2$

Correct answer:

$5184 \text{ inches}^3$ $\displaystyle 5184 \text{ inches}^3$

Explanation:

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

$V = l \cdot w \cdot h$ $\displaystyle V = l \cdot w \cdot h$

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

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

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

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

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Example Question #13 : 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 $\displaystyle 19ft^3$

$\displaystyle 144 ft^3$

36ft^3 $\displaystyle 36ft^3$

24ft^3 $\displaystyle 24ft^3$

Correct answer:

$\displaystyle 144 ft^3$

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:

$\displaystyle V=length*width*height$

$\displaystyle V=4ft*12ft*3ft=12ft*12ft^2=144ft^3$

So our answer is:

$\displaystyle 144 ft^3$

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Example Question #1 : Finding Volume Of A Rectangular Prism

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

Possible Answers:

Insufficient information is given to answer the question.

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

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

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

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

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

Correct answer:

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

Explanation:

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

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

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

$90\%$ $\displaystyle 90\%$ of this is

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

This rounds to $8\textup,300$ $\displaystyle 8\textup,300$ 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 #61 : Volume

Example Question #11 : Volume Of A Rectangular Solid

Example Question #62 : Volume

Example Question #14 : 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 #1 : Finding Volume Of A Rectangular Prism

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