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A cube has a side length of meters. What is the volume of the cube?

$8\ \textup{m}^{3}$

$6\ \textup{m}^{3}$

$4\ \textup{m}^{3}$

$2\ \textup{m}^{3}$

$16\ \textup{m}^{3}$

Explanation

The formula for the volume of a cube is:

$Volume = (side)^{3}$

Since the length of one side is meters, the volume of the cube is:

$2^{3 } = 8$ meters cubed.

A sphere with a radius of is cut out of a cube that has a side edge of . What is the volume of the resulting shape?

Explanation

Since the cube is bigger, we will be subtracting the volume of the sphere from the volume of the cube.

Start by recalling how to find the volume of a sphere.

$\text{Volume of Sphere}=\frac{4}{3}\pi r^3$

Plug in the given radius to find the volume.

$\text{Volume of Sphere}=\frac{4}{3}\pi(2)^3=\frac{32}{3}\pi$

Next, recall how to find the volume of a cube:

$\text{Volume of Cube}=(\text{edge})^3$

Plug in the given side length to find the volume of the cube.

$\text{Volume of Cube}=4^3=64$

Finally, subtract the volume of the sphere from the volume of the cube.

$\text{Volume of Figure}=64-\frac{32}{3}\pi=30.49$

Make sure to round to places after the decimal.

A sphere with a radius of is cut out of a cube that has a side edge of . What is the volume of the resulting shape?

Explanation

Since the cube is bigger, we will be subtracting the volume of the sphere from the volume of the cube.

Start by recalling how to find the volume of a sphere.

$\text{Volume of Sphere}=\frac{4}{3}\pi r^3$

Plug in the given radius to find the volume.

$\text{Volume of Sphere}=\frac{4}{3}\pi(2)^3=\frac{32}{3}\pi$

Next, recall how to find the volume of a cube:

$\text{Volume of Cube}=(\text{edge})^3$

Plug in the given side length to find the volume of the cube.

$\text{Volume of Cube}=4^3=64$

Finally, subtract the volume of the sphere from the volume of the cube.

$\text{Volume of Figure}=64-\frac{32}{3}\pi=30.49$

Make sure to round to places after the decimal.

If the surface area of a cube equals 96, what is the length of one side of the cube?

Explanation

The surface area of a cube = 6a2 where a is the length of the side of each edge of the cube. Put another way, since all sides of a cube are equal, a is just the lenght of one side of a cube.

We have 96 = 6a2 → a2 = 16, so that's the area of one face of the cube.

Solving we get √16, so a = 4

Find the length of an edge of the following cube:

Length_of_edge

The volume of the cube is $27\ m^3$ .

$3\ m$

$6\ m$

$9\ m$

$12\ m$

$15\ m$

Explanation

The formula for the volume of a cube is

where is the length of the edge of a cube.

Plugging in our values, we get:

$27\ m^3 = (e)^3$

$e = 3\ m$

A sphere with a radius of is cut out of a cube that has a side length of . What is the volume of the resulting figure?

Explanation

Since the cube is bigger, we will be subtracting the volume of the sphere from the volume of the cube.

Start by recalling how to find the volume of a sphere.

$\text{Volume of Sphere}=\frac{4}{3}\pi r^3$

Plug in the given radius to find the volume.

$\text{Volume of Sphere}=\frac{4}{3}\pi(1)^3=\frac{4}{3}\pi$

Next, recall how to find the volume of a cube:

$\text{Volume of Cube}=(\text{edge})^3$

Plug in the given side length to find the volume of the cube.

$\text{Volume of Cube}=5^3=125$

Finally, subtract the volume of the sphere from the volume of the cube.

$\text{Volume of Figure}=125-\frac{4}{3}\pi=120.81$

Make sure to round to places after the decimal.

If the surface area of a cube is , find the length of one side of the cube.

$6\sqrt2$

$8\sqrt3$

Explanation

Recall how to find the surface area of a cube:

$\text{Surface Area}=6(\text{side length})^2$

Since the question asks you to find the length of a side of this cube, rearrange the equation.

$\text{side length}^2=\frac{\text{Surface Area}}{6}$

$\text{side length}=\sqrt{\frac{\text{Surface Area}}{6}}$

Substitute in the given surface area to find the side length.

$\text{side length}=\sqrt{\frac{96}{6}}$

Simplify.

$\text{side length}=\sqrt{16}$

Reduce.

$\text{side length}=4$

Our backyard pool holds 10,000 gallons. Its average depth is 4 feet deep and it is 10 feet long. If there are 7.48 gallons in a cubic foot, how wide is the pool?

33 ft

30 ft

7.48 ft

100 ft

133 ft