Chapter E, Problem 12.8EX

To determine

To find: The correct option for the volume of cube.

Answer to Problem 12.8EX

The correct option is $\text{b}$ .

Explanation of Solution

Given information:

The radius of the cylinder is $5$ .

Calculation:

The diameter of the cylinder will be the diagonal of each face of cube.

  $2r=d$

Here, $r$ is the radius of cylinder, and $d$ is the diagonal of each face of cube.

Let, $a$ is the side of cube.

Calculate the side of the cube.

  $\begin{array}{c}d=\sqrt{2}a\\ \frac{d^2}{2}=a^2\\ a^2=\frac{d^2}{2}\\ a=\sqrt{\frac{100}{2}}\end{array}$

  $\begin{array}{c}a=\sqrt{50}\\ a=5\sqrt{2}\end{array}$

Calculate the volume of the cube.

  $\begin{array}{c}V=a^3\\ V={\left(5\sqrt{2}\right)}^3\\ V=250\sqrt{2}\end{array}$

Therefore, the correct option is B.