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Common Core: 7th Grade Math : Finding Volume of a Cube

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 #922 : Grade 7

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

Possible Answers:

500

384

512

Not enough information provided.

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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Example Question #1 : Finding Volume Of A Cube

Give the volume of a cube with surface area 150 square inches.

Possible Answers:

$250\textup{ in}^{3}$

$250\sqrt{3}\textup{ in}^{3}$

$125\textup{ in}^{3}$

$375\textup{ in}^{3}$

$125\sqrt{3}\textup{ in}^{3}$

Correct answer:

$125\textup{ in}^{3}$

Explanation:

Let be the length of one edge of the cube. Since its surface area is 150 square inches, one face has one-sixth of this area, or $\frac{150}{6} = 25$ square inches. Therefore, $s^{2} = 25$ , and s = 5 .

The volume is the cube of this, or $V= 5^{3}=125$ cubic inches.

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Example Question #1 : Finding Volume Of A Cube

Give the volume of a cube with surface area 240 square inches.

Possible Answers:

$120 \sqrt{10} \textup{ in}^{3}$

$80 \sqrt{10} \textup{ in}^{3}$

$120 \textup{ in}^{3}$

$80 \textup{ in}^{3}$

$40 \sqrt{10} \textup{ in}^{3}$

Correct answer:

$80 \sqrt{10} \textup{ in}^{3}$

Explanation:

Let be the length of one edge of the cube. Since its surface area is 240 square inches, one face has one-sixth of this area, or $\frac{240}{6} = 40$ square inches. Therefore, $s^{2} = 40$ , and $s = \sqrt{40} = 2\sqrt{10}$ .

The volume is the cube of this, or $V= \left ( 2\sqrt{10} \right )^{3}= 2^{3} \cdot \left ( \sqrt{10} \right )^{3}= 8 \cdot 10 \sqrt{10}= 80 \sqrt{10}$ cubic inches.

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Example Question #2 : Finding Volume Of A Cube

Calculate the volume of the provided figure.

Possible Answers:

$343\textup{ in}^3$

$345\textup{ in}^3$

$344\textup{ in}^3$

$341\textup{ in}^3$

$342\textup{ in}^3$

Correct answer:

$343\textup{ in}^3$

Explanation:

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

$V=l\times w\times h$

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

$V=7\times7\times7$

$V=343\textup{ in}^3$

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Example Question #3 : Finding Volume Of A Cube

Calculate the volume of the provided figure.

Possible Answers:

$216\textup{ in}^3$

$212\textup{ in}^3$

$215\textup{ in}^3$

$214\textup{ in}^3$

$213\textup{ in}^3$

Correct answer:

$216\textup{ in}^3$

Explanation:

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

$V=l\times w\times h$

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

$V=6\times6\times6$

$V=216\textup{ in}^3$

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Example Question #4 : Finding Volume Of A Cube

Calculate the volume of the provided figure.

Possible Answers:

$1\textup,332\textup{ in}^3$

$1\textup,333\textup{ in}^3$

$1\textup,335\textup{ in}^3$

$1\textup,334\textup{ in}^3$

$1\textup,331\textup{ in}^3$

Correct answer:

$1\textup,331\textup{ in}^3$

Explanation:

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

$V=l\times w\times h$

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

$V=11\times11\times11$

$V=1\textup,331\textup{ in}^3$

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Common Core: 7th Grade Math : Finding Volume of a Cube

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

All Common Core: 7th Grade Math Resources

Example Questions

Example Question #922 : Grade 7

Example Question #2 : Volume Of A Rectangular Solid

Example Question #1 : Finding Volume Of A Cube

Example Question #1 : Finding Volume Of A Cube

Example Question #2 : Finding Volume Of A Cube

Example Question #3 : Finding Volume Of A Cube

Example Question #4 : Finding Volume Of A Cube

All Common Core: 7th Grade Math Resources

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