How to find the volume of a cube

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Math › How to find the volume of a cube

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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 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.

The side length of a cube is ft.

What is the volume?

Explanation

The volume of a cube is

So with a side length of 2 ft, the volume is

$V = 2^{3}, ft^3 = 8, ft^3$

What is the volume of a cube with a side length of 7?

Explanation

When searching for the volume of a cube we are looking for the amount of the space enclosed by the cube.

To find this we must know the formula for the volume of a cube which is $Volume: of: Cube=s^{3}$

Using this formula we plug in the side length for to get $V=7^{3}$

Cube the side length to arrive at the answer of $7^{3}=343$

The answer is .

A rectangular prism with a square base is cut out of a cube as shown by the figure below.

Find the volume of the figure.

Explanation

Start by finding the volume of the cube.

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

$\text{Volume of Cube}=13^3=2197$

Next, find the volume of the rectangular prism.

$\text{Volume of Rectangular Prism}=\text{width}\times\text{length}\times\text{height}$

$\text{Volume of Rectangular Prism}=2 \times 2 \times 13=52$

Subtract the volume of the rectangular prism from that of the cube to find the volume of the figure.

$\text{Volume of Figure}=\text{Volume of Cube}-\text{Volume of Rectangular Prism}$

$\text{Volume of Figure}=2197- 52=2145$

A cube has a surface area of units squared. What is its volume?

units cubed

Explanation

Since a cube has square faces and the surface area of each face is given by multiplying the length of one side of the square face by itself, the equation for the surface area of a cube is , where is the length of one side of one face (i.e., one edge of the cube). Find the length of one side/edge of the given cube by setting the given surface area equal to :

$\rightarrow s^2 = 49$

$\rightarrow s = 7$ units

The volume of a cube is , where is the length of one of the cube's edges. Substituing the solution to the previous equation for in the volume equation gives the volume of the cube:

$\rightarrow V = (7)^3$

$\rightarrow V = 343$ units cubed

This figure is a cube with one face having an area of 16 in2. Cube

What is the volume of the cube (in3)?

Explanation

The volume of a cube is one side cubed. Because we know that one face has an area of 16 in2, then we know that one side must be the square root of 16 or 4. Thus the volume is $4^{3}=64$ .