A cone, a hemisphere and a cylinder stand on equal bases and have the

1.	A cone, a hemisphere and a cylinder stand on equal bases and have the same height. Show that their volumes are in the ratio 1 : 2 : 3.
Answer» Volume of a hemisphere = \(\frac{2}{3}\)πr³ Volume of a right circular cone = \(\frac{1}{3}\)πr²h Given, a cone, a hemisphere and a cylinder stand on equal bases and have the same height. Height of a hemisphere is the radius and equal bases implies equal base radius. Thus, height of cone = height of cylinder = base radius = r Ratio of volumes = \(\frac{1}{3}\)πr²h : \(\frac{2}{3}\)πr³ : πr²h ⇒ Ratio of volumes = r³ : 2r³ : 3r³ = 1 : 2 : 3

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

Answer»

Volume of a hemisphere = \(\frac{2}{3}\)πr³

Volume of a right circular cone = \(\frac{1}{3}\)πr²h

Given,

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

Height of a hemisphere is the radius and equal bases implies equal base radius.

Thus,

height of cone = height of cylinder = base radius = r

Ratio of volumes = \(\frac{1}{3}\)πr²h : \(\frac{2}{3}\)πr³ : πr²h

⇒ Ratio of volumes = r³ : 2r³ : 3r³ = 1 : 2 : 3