GED Math : Volume of a Rectangular Solid

Study concepts, example questions & explanations for GED Math

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Example Questions

Example Question #21 : 3 Dimensional Geometry

An aquarium takes the shape of a rectangular prism 60 centimeters high, 60 centimeters wide,  and 120 centimeters long. One-fourth of a cubic meter of water is poured into the aquarium after it has been emptied. How much more water can it hold?

Possible Answers:

\(\displaystyle 182,000 \textrm{ cm}^{3}\)

\(\displaystyle 429,500\textrm{ cm}^{2}\)

\(\displaystyle 407,000\textrm{ cm}^{2}\)

\(\displaystyle 702,000\textrm{ cm}^{2}\)

Correct answer:

\(\displaystyle 182,000 \textrm{ cm}^{3}\)

Explanation:

One cubic meter of water is equal to \(\displaystyle 100^{3} = 1,000,000\) cubic centimeters; one-fourth of a cubic meter is 250,000 centimeters. The volume of the aquarium is 

\(\displaystyle 60 \times 60 \times 120 = 432,000\) cubic centimeters.

Therefore, after having one-fourth of a cubic meter of water poured in, there is room left for 

\(\displaystyle 432,000 - 250,000 = 182,000\) cubic centimeters of water.

Example Question #1 : Volume Of A Rectangular Solid

A large aquarium has a rectangular base nine meters square and is ten and one-half meters high. The eight inlet pipes used to fill the aquarium does so at a rate of 200 liters per minute each. To the nearest hour, how long does it take for all eight pipes working together to fill the aquarium to 80% capacity?

You will need the conversion factor 1 liter = 1,000 cubic centimeters.

Possible Answers:

\(\displaystyle 71\textup{ hrs}\)

\(\displaystyle 7\textup{ hrs}\)

\(\displaystyle 9\textup{ hrs}\)

\(\displaystyle 57\textup{ hrs}\)

Correct answer:

\(\displaystyle 7\textup{ hrs}\)

Explanation:

The aquarium is a rectangular prism with dimensions 9 meters by 9 meters by 10.5 meters, each of which can be converted to centimeters by multiplying by 100. So the dimensions are 900 cm x 900 cm x 1,050 cm, and the volume is the product of the three, or

\(\displaystyle 900 \times 900 \times 1,050 = 850,500,000 \textup{ cm}^{3}\)

or

\(\displaystyle 850,500,000 \textup{ cm}^{3} \div 1,000 = 850,500 \textup{ L}\)

80% of this is

\(\displaystyle 850,500 \textup{ L } \times 80 \% = 680,400\textup{ L}\)

Each pipe fills the aquarium at 200 L per minute, so the eight pipes working together fill it at a rate of 1,600 L per minute. Divide, and the aquarium is filled at 80% capacity in

\(\displaystyle 680,400\textup{ L } \div 1,600 \textup{ L \ min}= 425.25\textup{ min}\)

In hours, this is

\(\displaystyle 425.25 \div 60 \approx 7.1\) 

so 7 hours is the correct response.

Example Question #1 : Volume Of A Rectangular Solid

If a swimming pool is rectangular, and its base area is 20 feet squared, what is the volume if the height of the pool is 8 feet?

Possible Answers:

\(\displaystyle 160 \textup{ ft}^3\)

\(\displaystyle 16\sqrt{5} \textup{ ft}^3\)

\(\displaystyle 160 \textup{ ft}^2\)

\(\displaystyle 80 \textup{ ft}^3\)

\(\displaystyle 80 \textup{ ft}^2\)

Correct answer:

\(\displaystyle 160 \textup{ ft}^3\)

Explanation:

The volume of the rectangular solid can be written as:

\(\displaystyle V= (LW)H = BH\)

The length times width constitutes the base of the rectangular solid, and is given in the question.

Substitute the known dimensions into the formula.

\(\displaystyle V= 20\textup{ ft}^2(8 \textup{ ft}) = 160 \textup{ ft}^3\)

The answer is:  \(\displaystyle 160 \textup{ ft}^3\)

Example Question #32 : 3 Dimensional Geometry

A rectangular wood block has the dimensions of 6 inches, 1 foot, and 8 inches.  What is the volume in feet?

Possible Answers:

\(\displaystyle 48\textup{ ft}^3\)

\(\displaystyle \frac{1}{3}\textup{ ft}^3\)

\(\displaystyle 6\textup{ ft}^3\)

\(\displaystyle \textup{The answer is not given.}\)

\(\displaystyle \frac{2}{3}\textup{ ft}^3\)

Correct answer:

\(\displaystyle \frac{1}{3}\textup{ ft}^3\)

Explanation:

Convert all the dimensions into feet.

\(\displaystyle 6 \textup{ inches} = \frac{1}{2} \textup{ ft}\)

\(\displaystyle 8 \textup{ inches} = \frac{8}{12} \textup{ ft}=\frac{2}{3} \textup{ ft}\)

Write the formula for the volume of the block.

\(\displaystyle V= LWH\)

Substitute the dimensions and solve for volume.

\(\displaystyle V= (\frac{1}{2} \textup{ ft})(\frac{2}{3} \textup{ ft})(1\textup{ ft}) = \frac{1}{3}\textup{ ft}^3\)

The answer is:  \(\displaystyle \frac{1}{3}\textup{ ft}^3\)

Example Question #31 : 3 Dimensional Geometry

Find the volume of a rectangular wood block with a length of \(\displaystyle 6\), width of \(\displaystyle \frac{1}{2}\), and a height of \(\displaystyle \frac{1}{3}\).

Possible Answers:

\(\displaystyle 1\)

\(\displaystyle 12\)

\(\displaystyle \frac{6}{5}\)

\(\displaystyle \frac{41}{6}\)

\(\displaystyle 4\)

Correct answer:

\(\displaystyle 1\)

Explanation:

Write the formula for the volume of a rectangular prism.

\(\displaystyle A=LWH\)

Substitute the dimensions into the formula.

\(\displaystyle A=6(\frac{1}{2})(\frac{1}{3}) = 6(\frac{1}{6}) = 1\)

The answer is:  \(\displaystyle 1\)

Example Question #6 : Volume Of A Rectangular Solid

Determine the volume of a brick in inches if its dimensions are 3 inches by 6 inches by 2 inches.

Possible Answers:

\(\displaystyle 72 \textup{ in}^3\)

\(\displaystyle 18 \textup{ in}^3\)

\(\displaystyle 36 \textup{ in}^2\)

\(\displaystyle 18 \textup{ in}^2\)

\(\displaystyle 36 \textup{ in}^3\) 

Correct answer:

\(\displaystyle 36 \textup{ in}^3\) 

Explanation:

The volume of a rectangular prism can be represented as:

\(\displaystyle V= LWH\)

Substitute the dimensions into the formula.

\(\displaystyle V = (3 \textup{ in}) (6 \textup{ in}) (2 \textup{ in}) = 36 \textup{ in}^3\)

Be sure that inches is cubed for volume.

The answer is:  \(\displaystyle 36 \textup{ in}^3\)

Example Question #2 : Volume Of A Rectangular Solid

What is the volume of a brick with a length of 6 inches, width of 4 inches, and a height of 3 inches?

Possible Answers:

\(\displaystyle 72\textup{ in}^2\)

\(\displaystyle 36\textup{ in}^3\)

\(\displaystyle 27\textup{ in}^3\)

\(\displaystyle 72\textup{ in}\)

\(\displaystyle 72\textup{ in}^3\)

Correct answer:

\(\displaystyle 72\textup{ in}^3\)

Explanation:

The volume of a brick is similar to finding the volume of a rectangular solid.

The volume for a rectangular solid is:

\(\displaystyle A=LWH\)

Substitute the dimensions.

\(\displaystyle A =(6\textup{ in})(4\textup{ in})(3\textup{ in}) = 72\textup{ in}^3\)

The answer is:  \(\displaystyle 72\textup{ in}^3\)

Example Question #2 : Volume Of A Rectangular Solid

Find the volume of the rectangular solid with a length, width, and height of 4,5,and 6, respectively.

Possible Answers:

\(\displaystyle 30\)

\(\displaystyle 360\)

\(\displaystyle 120\)

\(\displaystyle 720\)

\(\displaystyle 240\)

Correct answer:

\(\displaystyle 120\)

Explanation:

Write the volume for the rectangular solid.

\(\displaystyle V=LWH\)

Substitute the dimensions into the formula.

\(\displaystyle V = 4\times 5\times 6 = 120\)

The answer is:  \(\displaystyle 120\)

Example Question #2 : Volume Of A Rectangular Solid

Find the volume of a rectangular solid if the length, width, and height are 6, 12, and 20, respectively.

Possible Answers:

\(\displaystyle 1440\)

\(\displaystyle 448\)

\(\displaystyle 720\)

\(\displaystyle 2880\)

\(\displaystyle 960\)

Correct answer:

\(\displaystyle 1440\)

Explanation:

Write the volume for a rectangular solid.

\(\displaystyle V=LWH\)

Substitute the dimensions into the formula.

\(\displaystyle V= 6\times 12\times 20 = 1440\)

The answer is:  \(\displaystyle 1440\)

Example Question #583 : Geometry And Graphs

What is the volume of a book with a length of 7 inches, width of 4 inches, and a height of 1 inches?

Possible Answers:

\(\displaystyle 28\textup{ in}\)

\(\displaystyle 11\textup{ in}^3\)

\(\displaystyle 29\textup{ in}^3\)

\(\displaystyle 12\textup{ in}^3\)

\(\displaystyle 28\textup{ in}^3\)

Correct answer:

\(\displaystyle 28\textup{ in}^3\)

Explanation:

The book resembles a rectangular solid.  Write the formula for the volume of a rectangular solid.

\(\displaystyle V= LWH\)

Substitute the dimensions into the equation.

\(\displaystyle V= (7 \textup{ in})(4\textup{ in})(1\textup{ in}) = 28\textup{ in}^3\)

The answer is:  \(\displaystyle 28\textup{ in}^3\)

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