Question

A cube is inscribed in a sphere. A right circular cylinder is within the cube touching all the vertical faces. A right circular

once is inside the cylinder. Their heights are same and the diameter of the cone is equal to that of the

cylinder.

What is the ratio of the volume of the cube to that of the cylinder?

Answer 1

Answer:

$4:\pi$

Step-by-step explanation:

Let the length of a side of of the cube be a

Then the volume of the Cube = $a^3$

The height of the cylinder as well as the cone will be a

The diameter of the base will also be a

thus the Volume of the cylinder will be

$=\pi(\frac{a}{2})^2\times a$

$=\pi(\frac{a^3}{4})$

$=\frac{\pi a^3}{4}$

Ratio of the volume of the cube to that of cylinder

$=\frac{a^3}{\pi a^3/4}$

$=\frac{4}{\pi}$

$=4:\pi$

Hope this helps.