Question

A cone​​,a hemisphere and a cylinder satand on equal bases and have the same height.Show that their volumes ate in the ratio 1:2:3.​

Answer 1

Given:

A cone​​, a hemisphere and a cylinder stand on equal bases and have the same height.

To prove: The volumes of the above solids are in the ratio 1:2:3

Proof:

Volume of cone = $\frac{1}{3}$πr²h

Volume of hemisphere = $\frac{2}{3}$πr²h

Volume of cylinder = πr²h

Cone:Hemisphere:Cylinder

= $\frac{1}{3}$πr²h:$\frac{2}{3}$πr²h:πr²h

= $\frac{1}{3}$:$\frac{2}{3}$:1

= $\frac{1}{3}$ ÷ $\frac{2}{3}$ ÷ 1

= $\frac{1}{3}$ ÷ $\frac{2}{3}$ ÷ $\frac{3}{3}$

= 1 ÷ 2 ÷ 3

= 1:2:3

Hence Proved!