Question

A cone, a hemisphere and a cylinder stand on equal bases and have the same height . find the ratio of their volume.​

Answer 1

Hey Shubham !

Answer:

h : 2r : 3h (OR) 1 : 2 : 3 [If r = h]

Step-by-step explanation:

Given :

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

i.e. r and h, both are same for all.

To Find :

Find the ratio of their volumes.

Formulae :

Volume of a Cone = (1/3)πr²h units³.

• Where r is the Radius of the Base of the Cone and h is the Height.

Volume of a Hemisphere = (2/3)πr³ units³.

• Where r is the Radius.

Volume of a Cylinder = πr²h units³.

• Where r is the Radius of the Base of the Cylinder and h is the Height.

Procedure :

Ratio of the volumes of Cone, Hemisphere and Cylinder is

(1/3)πr²h units³ : (2/3)πr³ units³ : πr²h units³

⇒ (1/3)r²h : (2/3)r³ : r²h

Multiplying by 3,

⇒ r²h : 2r³ : 3r²h

⇒ h : 2r : 3h

If r = h,

⇒ r³ : 2r³ : 3r³

∴ 1 : 2 : 3 is the ratio.

Thanks !