Question

Calculate the approximate edge length of a cube having the same volume as a sphere of radius $5$cm.

• A. $5.00$
• B. $5.50$
• C. $6.24$
• D. $8.06$

Answer 1

Answer: (D)

$8.06$

Let the length of edge and radius are $a$ and $r$ respectively.

Given, $r=5$

Volume of cube of edge length $a$ is $a^3$.

Volume of sphere of radius $r$ is $\frac{4}{3}\pi r^3$.

$=\frac{4}{3}\times \frac{22}{7}\times 5^3=523.8095238c{m}^3$

Both the volume of the cube and sphere are equal.

So, $a^3=523.809$

$\Rightarrow a=8.06cm$