Question

the ratio of surface area of a sphere and curved surface area of hemisphere is 9:2 find ratio of their volume​

Answer 1

Answer:

the ratio of surface area of a

sphere and curved surface

area of a hemisphere is 9:2

Then ratio of their volumes = 27:4

Step-by-step explanation:

surface area of a sphere =  4πR₁²

curved surface area of a hemisphere =  2πR₂²

surface area of a sphere/curved surface area of a hemisphere = 4πR₁²/2πR₂²

= 2R₁²/R₂²

2R₁²/R₂² = 9/2

=> R₁²/R₂² = 9/4

=> R₁²/R₂² = 3²/2²

=> R₁/R₂ = 3/2

Volume of sphere = (4/3)πR₁³

Volume of Hemisphere = (2/3)πR₂³

Volume of sphere /Volume of Hemisphere  = ((4/3)πR₁³)/((2/3)πR₂³)

= 2 (R₁/R₂)³

= 2 (3/2)³

= 27/4

Ratio of their volumes = 27:4