Question

ratio of surface area of sphere and curved surface area of hemisphere is 9 ratio 2 find the ratio of their volumes​

Answer 1

Formula required:

Surface area of a sphere is 4 πR^2

Curved Surface area of a hemisphere is 2 πr^2

Volume of a sphere is 4/3 πR^3

Volume of hemisphere is 2/3 πr^3

Where,

R is radius of sphere

r is radius of hemisphere.

Given:

Ratio of surface area of sphere and curved surface area of hemisphere = 9:2

So,

4 πR^2 / 2πr^2 = 9/2

2 * R^2 / r^2 = 9/2  ------- (1)

Now, ratio of their volumes will be,

4/3 πR^3 / 2/3 πr^3 = 2 R^3/r^3

 2 * (R/r) * R^2 / r^2

 (R/r) * 9/2   ( by replacing from equation (1)

Answer:

Ratio of the volumes = 9R/2r