Question

The volume of a cube is 9261000 m³. Find the side of the cube.

 

Answer 1

Volume of a cube is given by: \[V = s^3\], where s = Side of the cube

It is given that the volume of the cube is 9261000 m³; therefore, we have: \[s^3 = 9261000\]

Let us find the cube root of 9261000 using prime factorisation:

\[9261000 = 2 \times 2 \times 2 \times 3 \times 3 \times 3 \times 5 \times 5 \times 5 \times 7 \times 7 \times 7 = \left\{ 2 \times 2 \times 2 \right\} \times \left\{ 3 \times 3 \times 3 \right\} \times \left\{ 5 \times 5 \times 5 \right\} \times \left\{ 7 \times 7 \times 7 \right\}\]

9261000 could be written as a triples of equal factors; therefore, we get:
Cube root =  \[2 \times 3 \times 5 \times 7 = 210\]

Therefore

\[s^3 = 9261000 \Rightarrow s = \sqrt[3]{9261000} = 210\]

Hence, the length of the side of cube is 210 m.