2. The ratio of surface area of a sphere and curved surfacearea of a h

1.	2. The ratio of surface area of a sphere and curved surfacearea of a hemisphere is 9:2. Find ratio of their volumes.
Answer» CSA of hemisphere = 2πr² [r= radius of hemisphere] CSA of sphere = 4πR² [R=radius of sphere] thus ratio of their CSA= 2:9 ∴2/9 = 2πr²/4πR² 2/9= r²/2R² 2/9×2R²=r² 2×2R²=9×r² 4R²=9r² r²/R²=4/9 r/R=√4/√9 ∴r/R=2/3 ratio of the radii of the hemisphere and sphere r:R=2:3

2. The ratio of surface area of a sphere and curved surfacearea of a hemisphere is 9:2. Find ratio of their volumes.

Answer»

CSA of hemisphere = 2πr² [r= radius of hemisphere]

CSA of sphere = 4πR² [R=radius of sphere]

thus ratio of their CSA= 2:9

∴2/9 = 2πr²/4πR²

2/9= r²/2R²

2/9×2R²=r²

2×2R²=9×r²

4R²=9r²

r²/R²=4/9

r/R=√4/√9

∴r/R=2/3

ratio of the radii of the hemisphere and sphere

r:R=2:3