Since the hemispherical tank is made of 1 cm thick iron, we can find the outer radius of the tank by adding thickness to the inner radius.
The Volume of a hemisphere of base radius, r = 2/3π r3
The inner radius of the tank, r = 1m
Thickness of iron = 1cm = 1/100 m = 0.01 m
Outer radius of the tank, R = 1 m + 0.01m = 1.01m
The volume of the iron used to make the tank can be calculated by subtracting the volume of the tank with inner radius from the volume of the tank with outer radius.
Volume of the iron used to make the tank = 2/3π R3 - 2/3π r3
= 2/3π (R3 - r3)
= 2/3 × 22/7 × [(1.01m)3 - (1m)3]
= 2/3 × 22/7 × [1.030301 m3 - 1 m3]
= 2/3 × 22/7 × 0.030301 m3
= 0.06348 m3 (approx.)
0.06348 m3 of iron used to make the tank.
