Shown alongside is a horizontal water tank composed of a cylinder and two hemispheres. The tank is filled up to a height of 7 m. Find the surface area of the tank in contact with water. Use $\pi = \frac{22}{7}$.
Show SolutionHide Solution↓
From figure,
Radius of cylindrical part = Radius of hemispherical part = r = 7 m.
Length (Height h) of the cylindrical part = 34 - 7 - 7 = 20 m.
Surface of cylindrical part in contact of water
= $\frac{1}{2} \times 2πrh = \frac{1}{2} \times 2 \times \frac{22}{7} \times 7 \times 20$ = 440 m2
Surface of each hemisphere in contact of water
= $\frac{1}{2} \times 2πr^2$
= πr2
= $\frac{22}{7} \times 7^2$
= 22 × 7
= 154 m2.
∴ Surface area of the tank in contact of water = 440 + 2 × 154
= 440 + 308
= 748 m2.
Hence, surface area of tank in contact with water = 748 m2.