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A hemispherical tank is made up of an iron sheet 1 cm thick. If the inner radius is 1 m, then find the volume of the iron used to make the tank.

Q : 6    A hemispherical tank is made up of an iron sheet 1 cm thick. If the inner radius is 1 m, then find the volume of the iron used to make the tank. 

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Given,

Inner radius of the hemispherical tank = r_1 = 1\ m

Thickness of the tank = 1\ cm = 0.01\ m

\therefore Outer radius = Internal radius + thickness = r_2 = (1+0.01)\ m = 1.01\ m

We know, Volume of a hemisphere = \frac{2}{3}\pi r^3

\therefore Volume of the iron used = Outer volume - Inner volume 

= \frac{2}{3}\pi r_2^3 - \frac{2}{3}\pi r_1^3

= \frac{2}{3}\times\frac{22}{7}\times (1.01^3 - 1^3)

= \frac{44}{21}\times0.030301

= 0.06348\ m^3\ \ (approx)

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