Math - How to find the volume of a cube

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 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

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 .

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 $4^{3}=64$ .

What is the difference in volume between a sphere with radius x and a cube with a side of 2x? Let π = 3.14

3.82x3

8.00x3

5.28x3

4.18x3

6.73x3

Explanation

Vcube = s3 = (2x)3 = 8x3

Vsphere = 4/3 πr3 = 4/3•3.14•x3 = 4.18x3

A cube has edges that are three times as long as those of a smaller cube. The volume of the bigger cube is how many times larger than that of the smaller cube?

Explanation

If we let represent the length of an edge on the smaller cube, its volume is $x^{3}$ .

The larger cube has edges three times as long, so the length can be represented as . The volume is $(3x)^{3}$ , which is $27x^{3}$ .

The large cube's volume of $27x^{3}$ is 27 times as large as the small cube's volume of $x^{3}$ .

The density of gold is $16\ g/cm^3$ and the density of glass is $2\ g/cm^3$ . You have a gold cube that is $x\ cm$ in length on each side. If you want to make a glass cube that is the same weight as the gold cube, how long must each side of the glass cube be?

Explanation

Weight = Density * Volume

Volume of Gold Cube = side3= x3

Weight of Gold = 16 g/cm3 * x3

Weight of Glass = 3/cm3 * side3

Set the weight of the gold equal to the weight of the glass and solve for the side length:

16* x3 = 2 * side3

side3 = 16/2* x3 = 8 x3

Take the cube root of both sides:

side = 2x

If the length of the side of a cube is $8x^{2}$ , which expression represents the volume of the cube?

$512x^{6}$

$8x^{3}$

$64x^{6}$

$512x^{3}$

none of the other answers

Explanation

The formula for the volume of the cube is $V = x^{3}$

Plugging that into Volume equation, we find $8^{3}$ and $(x^{^{2)^{3}}}$

Thus, the answer is 512x6

Find the volume of the following cube:

Length_of_diagonal

$64\ m^3$

$60\ m^3$

$56\ m^3$

$68\ m^3$

$52\ m^3$

Explanation

The formula for the volume of a cube is

where is the side of the cube.

Plugging in our values, we get:

$V=(4\ m)^3$

$V=64\ m^3$

What is the volume, in centimeters, of a rectangular prism with a length of , a width of , and a height of ?

$2692.8cm^{3}$

$\dpi{100} 2962.8cm^{3}$

$\dpi{100}269.28 cm^{3}$

$26928cm^{3}$

$2448.01cm^{3}$

Explanation

In order to solve this problem, we need to make sure that the measurements given are in uniform units. In this case, we will use centimeters; therefore, we need to convert the other units of meters and millimeters into centimeters via dimensional analysis.

Solve for the width.

$w=\frac{255mm}{1}*\frac{1cm}{10mm}$