Question

A water tank open at top is hemispherical at bottom and cylinder above it. If radius of hemisphere is 12m and total capacity of the tank is 3312π m cube. Find the ratio of surface area of hemispherical and cylindrical portion

Answer 1

Volume of tank=$3312 \pi cm ^{3}$
therefore,
 volume of tank=volume of cylindrical portion+volume of hemispherical portion
= $\pi r ^{2} h$+ 2/3 $\pi r ^{3}$=3312$\pi$
=$\pi r ^{2}$(2/3r+h)=3312 $\pi$
=12X12(2/3X12+h)=3312
=2/3X12+h=3312/144
=8+h=13
=h=5cm
therefore,
ratio of the surface areas is:-
CSA of hemispherical portion : CSA of cylindrical portion
2$\pi$rh : 2$\pi r^{2}$
h : r
5 : 12