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GED Math : Geometry and Graphs

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Example Questions

Example Question #1 : Volume Of A Rectangular Solid

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:

$407,000\textrm{ cm}^{2}$

$702,000\textrm{ cm}^{2}$

$429,500\textrm{ cm}^{2}$

$182,000 \textrm{ cm}^{3}$

Correct answer:

$182,000 \textrm{ cm}^{3}$

Explanation:

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

$60 \times 60 \times 120 = 432,000$ cubic centimeters.

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

432,000 - 250,000 = 182,000 cubic centimeters of water.

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Example Question #581 : Geometry And Graphs

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:

$57\textup{ hrs}$

$7\textup{ hrs}$

$9\textup{ hrs}$

$71\textup{ hrs}$

Correct answer:

$7\textup{ hrs}$

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

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

$850,500,000 \textup{ cm}^{3} \div 1,000 = 850,500 \textup{ L}$

80% of this is

$850,500 \textup{ L } \times 80 \% = 680,400\textup{ L}$

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

$680,400\textup{ L } \div 1,600 \textup{ L \ min}= 425.25\textup{ min}$

In hours, this is

$425.25 \div 60 \approx 7.1$

so 7 hours is the correct response.

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Example Question #2 : 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:

$80 \textup{ ft}^2$

$16\sqrt{5} \textup{ ft}^3$

$160 \textup{ ft}^2$

$80 \textup{ ft}^3$

$160 \textup{ ft}^3$

Correct answer:

$160 \textup{ ft}^3$

Explanation:

The volume of the rectangular solid can be written as:

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.

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

The answer is: $160 \textup{ ft}^3$

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Example Question #2 : Volume Of A Rectangular Solid

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

Possible Answers:

$6\textup{ ft}^3$

$\frac{1}{3}\textup{ ft}^3$

$\textup{The answer is not given.}$

$48\textup{ ft}^3$

$\frac{2}{3}\textup{ ft}^3$

Correct answer:

$\frac{1}{3}\textup{ ft}^3$

Explanation:

Convert all the dimensions into feet.

$6 \textup{ inches} = \frac{1}{2} \textup{ ft}$

$8 \textup{ inches} = \frac{8}{12} \textup{ ft}=\frac{2}{3} \textup{ ft}$

Write the formula for the volume of the block.

V= LWH

Substitute the dimensions and solve for volume.

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

The answer is: $\frac{1}{3}\textup{ ft}^3$

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Example Question #3 : Volume Of A Rectangular Solid

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

Possible Answers:

$\frac{6}{5}$

$\frac{41}{6}$

Correct answer:

Explanation:

Write the formula for the volume of a rectangular prism.

A=LWH

Substitute the dimensions into the formula.

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

The answer is:

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Example Question #3 : 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:

$18 \textup{ in}^3$

$36 \textup{ in}^2$

$18 \textup{ in}^2$

$72 \textup{ in}^3$

$36 \textup{ in}^3$

Correct answer:

$36 \textup{ in}^3$

Explanation:

The volume of a rectangular prism can be represented as:

V= LWH

Substitute the dimensions into the formula.

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

Be sure that inches is cubed for volume.

The answer is: $36 \textup{ in}^3$

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Example Question #4 : 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:

$72\textup{ in}$

$27\textup{ in}^3$

$36\textup{ in}^3$

$72\textup{ in}^3$

$72\textup{ in}^2$

Correct answer:

$72\textup{ in}^3$

Explanation:

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

The volume for a rectangular solid is:

A=LWH

Substitute the dimensions.

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

The answer is: $72\textup{ in}^3$

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Example Question #31 : 3 Dimensional Geometry

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

Possible Answers:

720

360

240

120

Correct answer:

120

Explanation:

Write the volume for the rectangular solid.

V=LWH

Substitute the dimensions into the formula.

$V = 4\times 5\times 6 = 120$

The answer is: 120

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Example Question #3 : 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:

2880

1440

960

448

720

Correct answer:

1440

Explanation:

Write the volume for a rectangular solid.

V=LWH

Substitute the dimensions into the formula.

$V= 6\times 12\times 20 = 1440$

The answer is: 1440

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Example Question #4 : Volume Of A Rectangular Solid

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:

$11\textup{ in}^3$

$29\textup{ in}^3$

$28\textup{ in}$

$12\textup{ in}^3$

$28\textup{ in}^3$

Correct answer:

$28\textup{ in}^3$

Explanation:

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

V= LWH

Substitute the dimensions into the equation.

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

The answer is: $28\textup{ in}^3$

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GED Math : Geometry and Graphs

Study concepts, example questions & explanations for GED Math

All GED Math Resources

Example Questions

Example Question #1 : Volume Of A Rectangular Solid

Example Question #581 : Geometry And Graphs

Example Question #2 : Volume Of A Rectangular Solid

Example Question #2 : 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

Example Question #31 : 3 Dimensional Geometry

Example Question #3 : Volume Of A Rectangular Solid

Example Question #4 : Volume Of A Rectangular Solid

All GED Math Resources

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