Question

A right circular cylinder of height $h$ is inscribed in a cube of height h so that the bases of the cylinder are inscribed in the upper and lower faces of the cube. The ratio of the volume of the cylinder to that of the cube is

• A. $\pi :4$
• B. $4\pi$
• C. $3:4$
• D. $2:3$
• E. $\pi :1$

Answer 1

The correct option is A $\pi :4$

The length of cube is equal to $h=2r$ wher $r$ is rqdius of base of cylinder
We get $r=\frac{h}{2}$
Volume of cylinder is $\pi \times \frac{h^2}{4}\times h=h^3\times \frac{\pi }{4}$
Volume of cube is $h^3$
The ratio of volume of cylinder to cube is $h^3\times \frac{\pi /4}{h^3}=\frac{\pi }{4}$