The volume of a cube is 9261000


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


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:


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=\{2 \times 2 \times 2\} \times\{3 \times 3 \times 3\} \times\{5 \times 5 \times 5\}$$\times\{7 \times 7 \times 7\}$

9261000 could be written as a triples of equal factors; therefore, we get:

Cube root $=2 \times 3 \times 5 \times 7=210$


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

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


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