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Common Core: 7th Grade Math : Finding Volume of a Rectangular Prism

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Example Questions

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 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:

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

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

Insufficient information is given to answer the question.

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

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

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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Example Question #17 : Solve Problems Involving Area, Volume And Surface Area Of Two And Three Dimensional Objects: Ccss.Math.Content.7.G.B.6

Calculate the volume of the provided figure.

Possible Answers:

$144\textup{ in}^3$

$141\textup{ in}^3$

$143\textup{ in}^3$

$145\textup{ in}^3$

$142\textup{ in}^3$

Correct answer:

$144\textup{ in}^3$

Explanation:

In order to solve this problem, we need to recall the volume formula for a rectangular prism:

$V=l\times w\times h$

Now that we have the correct formula, we can substitute in our known values and solve:

$V=9\times4\times4$

$V=144\textup{ in}^3$

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Example Question #1 : Finding Volume Of A Rectangular Prism

Calculate the volume of the provided figure.

Possible Answers:

$182\textup{ in}^3$

$180\textup{ in}^3$

$181\textup{ in}^3$

$183\textup{ in}^3$

$184\textup{ in}^3$

Correct answer:

$180\textup{ in}^3$

Explanation:

In order to solve this problem, we need to recall the volume formula for a rectangular prism:

$V=l\times w\times h$

Now that we have the correct formula, we can substitute in our known values and solve:

$V=12\times5\times3$

$V=180\textup{ in}^3$

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Example Question #2 : Finding Volume Of A Rectangular Prism

Calculate the volume of the provided figure.

Possible Answers:

$242\textup{ in}^3$

$243\textup{ in}^3$

$240\textup{ in}^3$

$244\textup{ in}^3$

$241\textup{ in}^3$

Correct answer:

$240\textup{ in}^3$

Explanation:

In order to solve this problem, we need to recall the volume formula for a rectangular prism:

$V=l\times w\times h$

Now that we have the correct formula, we can substitute in our known values and solve:

$V=10\times4\times6$

$V=240\textup{ in}^3$

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Example Question #3 : Finding Volume Of A Rectangular Prism

A rectangular prism has the following dimensions:

Length: $6.3 \:cm$

Width: $6.3 \:cm$

Height: $2.1 \:cm$

Find the volume.

Possible Answers:

$84.9\:cm^3$

$83.3\:cm^3$

$83.4\:cm^3$

$83.8\:cm^3$

$84.3\:cm^3$

Correct answer:

$83.3\:cm^3$

Explanation:

Given that the dimensions are: $6.3 \:cm$ , $6.3 \:cm$ , and $2.1 \:cm$ and that the volume of a rectangular prism can be given by the equation:

$v=l \cdot w \cdot h$ , where is length, is width, and is height, the volume can be simply solved for by substituting in the values.

V = (6.3)(6.3)(2.1)

V = (39.69)(2.1)

$V = 83.349\:cm^3$

This final value can be approximated to $83.3\:cm^3$ .

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Example Question #91 : Geometry

Solve for the volume of a prism that is 4m by 3m by 8m.

Possible Answers:

V=88m^3

V = 136 m^3

V = 102 m^3

V = 144 m^3

V = 96 m^3

Correct answer:

V = 96 m^3

Explanation:

The volume of the rectangle

V = l*w*h

so we plug in our values and obtain

V = 4*3*8

V = 96 m^3 .

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Example Question #91 : Geometry

The dimensions of Treasure Chest A are 39” x 18”. The dimensions of Treasure Chest B are 16” x 45”. Both are 11” high. Which of the following statements is correct?

Possible Answers:

There is insufficient data to make a comparison between Treasure Chest A and Treasure Chest B.

Treasure Chest A and B can hold the same amount of treasure.

Treasure Chest A has the same surface area as Treasure Chest B.

Treasure Chest B can hold more treasure.

Treasure Chest A can hold more treasure.

Correct answer:

Treasure Chest B can hold more treasure.

Explanation:

The volume of B is 7920 in³. The volume of A is 7722 in³. Treasure Chest B can hold more treasure.

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Example Question #5 : Finding Volume Of A Rectangular Prism

A rectangular prism has a width of 3 inches, a length of 6 inches, and a height triple its length. Find the volume of the prism.

Possible Answers:

38in^3

324in^3

27in^3

420in^3

Correct answer:

324in^3

Explanation:

A rectangular prism has a width of 3 inches, a length of 6 inches, and a height triple its length. Find the volume of the prism.

Find the volume of a rectangular prism via the following:

V=l*w*h

Where l, w, and h are the length width and height, respectively.

We know our length and width, and we are told that our height is triple the length, so...

h=3l=3*6in=18in

Now that we have all our measurements, plug them in and solve:

V=3in*6in*18in=324in^3

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Example Question #6 : Finding Volume Of A Rectangular Prism

Box

The above diagram shows a rectangular solid. The shaded side is a square. In terms of , give the volume of the box.

Possible Answers:

$4x^{2} + 30 x$

60x + 450

225x

$15x^{2}$

Correct answer:

225x

Explanation:

A square has four sides of equal length, as seen in the diagram below.

Box

The volume of the solid is equal to the product of its length, width, and height, as follows:

$V = 15 \cdot 15 \cdot x =225 x$ .

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Common Core: 7th Grade Math : Finding Volume of a Rectangular Prism

Study concepts, example questions & explanations for Common Core: 7th Grade Math

All Common Core: 7th Grade Math Resources

Example Questions

Example Question #1 : Finding Volume Of A Rectangular Prism

Example Question #17 : Solve Problems Involving Area, Volume And Surface Area Of Two And Three Dimensional Objects: Ccss.Math.Content.7.G.B.6

Example Question #1 : Finding Volume Of A Rectangular Prism

Example Question #2 : Finding Volume Of A Rectangular Prism

Example Question #3 : Finding Volume Of A Rectangular Prism

Example Question #91 : Geometry

Example Question #91 : Geometry

Example Question #5 : Finding Volume Of A Rectangular Prism

Example Question #6 : Finding Volume Of A Rectangular Prism

All Common Core: 7th Grade Math Resources

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