Question

Question 5
The volume of the largest right circular cone that can be fitted in a cube whose edge is 2r equals to the volume of a hemisphere of radius r.

Answer 1

True.

Given,
Edge of cube = 2r
The height of the cone becomes, h = 2r.

Volume of the cone
$=\frac{1}{3}\pi r^{2}h=\frac{1}{3}\pi r^2\left(2r\right)=\frac{2}{3}\pi r^3$

Volume of a hemisphere
$=\frac{2}{3}\pi r^3$

Hence, volumes of the cone and hemisphere are equal.