Cube of 4 – Value – Solved examples

Cube of 4 

The cube of a number is the product we get when the number is multiplied by itself three times. It is represented by the symbol x^3 (exponential form).

To find the cube of the number 4, we have to multiply 4 by itself three times as shown below.

Cube of 4=4^{3}

                 =4 \times 4 \times 4
                 =16 \times 4=64
 

The product of 4 when multiplied by itself 3 times is equal to 64. Hence the value of 4^{3} is equal to 64.

We can also write that 4^{3}=64.

Applications of  4^{3}

1. 64 is the value of 4^{3}. Therefore we can say that 4 is the cube root of 64.
2. 64 is a perfect cube.
3. If there is a cube with a side of length 4 units, then the volume of the cube is equal to the cube of side measuring 4 units i.e., 64 cubic units.

Solved Examples

1. Find the value of 4^{3}.

4^{3}=4 \times 4 \times 4=16 \times 4=64

Hence the value of 4^{3} is 64.

2. Find the value of 40^{3}.

40^{3}=(4 \times 10)^{3}=4^{3} \times 10^{3}

Putting the values of 4^{3} \text { and } 10^{3}:

40^{3} = 64 × 1000 = 64000

Hence the value of 40^{3} is 64000.

3. Find the value of 0.4^{3}.

0.4^{3}=\left(\frac{4}{10}\right)^{3}=\frac{4^{3}}{10^{3}}

Putting the values of 4^{3} \text { and } 10^{3}:

0.4^{3}=\frac{64}{1000}=0.064

Hence the value of 0.4^{3} is 0.064.

4. Find the volume of a cube having a side of 4 m?

Length of each side = 4 m

Volume of the cube =\operatorname{side}^{3}=4^{3}=64 \mathrm{~m}^{3}

5. Find the value of (-4)^{3}.

Putting the values of 4^{3} \text { and }(-1)^{3}:

Hence the value of (-4)^{3} \text { is }(-64).