7th Grade Math - Finding Volume of a Cube

Calculate the volume of the provided figure.

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

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

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

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

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

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:

$V=11\times11\times11$

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

Calculate the volume of the provided figure.

$343\textup{ in}^3$

$342\textup{ in}^3$

$341\textup{ in}^3$

$344\textup{ in}^3$

$345\textup{ in}^3$

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:

$V=7\times7\times7$

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

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

Not enough information provided.

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.

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

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

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

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

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

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

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

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 .

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

Calculate the volume of the provided figure.

$216\textup{ in}^3$

$215\textup{ in}^3$

$214\textup{ in}^3$

$213\textup{ in}^3$

$212\textup{ in}^3$

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:

$V=6\times6\times6$

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

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

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

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

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

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

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

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.