Question

A sphere and a cone have same radius if height of cone is equal to radius of cone . Fibd the relation between volume of cone and volume of sphere

Answer 1

Answer:

Volume of sphere= 4 x vol of cone.

Step-by-step explanation:

Let radius of cone be r.

Then,

Height of cone = r

{Since height of cone is same as radius of cone}

➡Volume of cone = 1/3 x π x radius^2 x height.

Volume = 1/3 x π x r^2 x r

➡Volume of cone = 1/3 π r^3

Now,

Radius of sphere = radius of cone

Radius of sphere= r

➡Volume of sphere = 4/3 x π x radius^3

Volume of sphere = 4/3 x π x r^3

➡Volume of sphere = 4/3 π r^3.

Dividing vol of sphere with vol of cone :

4/3 π r^3 x 3 x 1/ r^3

➡Vol sphere/ vol cone = 4/1

Or

➡Volume of sphere = 4 x volume of cone

Or

➡Volume sphere : vol cone = 4 :1.