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Common Core: 7th Grade Math : Grade 7

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

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All Common Core: 7th Grade Math Resources

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Example Questions

Example Question #2 : Finding Volume Of A Rectangular Prism

Calculate the volume of the provided figure.

Possible Answers:

$141\textup{ in}^3$

$145\textup{ in}^3$

$143\textup{ in}^3$

$144\textup{ in}^3$

$142\textup{ in}^3$

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 #3 : Finding Volume Of A Rectangular Prism

Calculate the volume of the provided figure.

Possible Answers:

$181\textup{ in}^3$

$183\textup{ in}^3$

$182\textup{ in}^3$

$180\textup{ in}^3$

$184\textup{ in}^3$

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 #4 : Finding Volume Of A Rectangular Prism

Calculate the volume of the provided figure.

Possible Answers:

$244\textup{ in}^3$

$241\textup{ in}^3$

$240\textup{ in}^3$

$242\textup{ in}^3$

$243\textup{ in}^3$

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 #2 : 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:

$84.9\:cm^3$

$83.8\:cm^3$

$83.4\:cm^3$

$84.3\:cm^3$

$83.3\:cm^3$

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 #1 : How To Find The Volume Of A Prism

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

Possible Answers:

V = 102 m^3

V = 144 m^3

V = 136 m^3

V=88m^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 #1 : Finding Volume Of A Rectangular Prism

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 has the same surface area as Treasure Chest B.

Treasure Chest B can hold more treasure.

Treasure Chest A can hold more treasure.

Treasure Chest A and B can hold the same amount of 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 #1 : 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

420in^3

27in^3

324in^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 #1 : 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:

225x

$4x^{2} + 30 x$

$15x^{2}$

60x + 450

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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Example Question #1 : Volume Of A Rectangular Solid

If a cube is inches tall, what is its volume?

Possible Answers:

Not enough information provided.

500

512

384

Correct answer:

512

Explanation:

To find the volume of a cube, we multiply length by width by height, which can be represented with the forumla $v=l\cdot w\cdot h$ . Since a cube has equal sides, we can use for all three values.

$8\cdot 8\cdot 8=512\: in ^{3}$

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Example Question #2 : Volume Of A Rectangular Solid

What is the volume of a cube with a side length equal to inches?

Possible Answers:

$343\: in^{3}$

$53\: in^{3}$

$21\: in^{3}$

$49\: in^{3}$

Correct answer:

$343\: in^{3}$

Explanation:

The volume of a a cube (or rectangular prism) can be solved using the following equation:

$V=l\times\ w\times\ h$

$V=7in\times 7in\times 7in=343in^3$

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Common Core: 7th Grade Math : Grade 7

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

All Common Core: 7th Grade Math Resources

Example Questions

Example Question #2 : Finding Volume Of A Rectangular Prism

Example Question #3 : Finding Volume Of A Rectangular Prism

Example Question #4 : Finding Volume Of A Rectangular Prism

Example Question #2 : Finding Volume Of A Rectangular Prism

Example Question #1 : How To Find The Volume Of A Prism

Example Question #1 : Finding Volume Of A Rectangular Prism

Example Question #1 : Finding Volume Of A Rectangular Prism

Example Question #1 : Finding Volume Of A Rectangular Prism

Example Question #1 : Volume Of A Rectangular Solid

Example Question #2 : Volume Of A Rectangular Solid

All Common Core: 7th Grade Math Resources

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