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

**Solution:**

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 r^{3}

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 R^{3} - 2/3π r^{3}

= 2/3π (R^{3} - r^{3})

= 2/3 × 22/7 × [(1.01m)^{3} - (1m)^{3}]

= 2/3 × 22/7 × [1.030301 m^{3} - 1 m^{3}]

= 2/3 × 22/7 × 0.030301 m^{3}

= 0.06348 m^{3} (approx.)

0.06348 m^{3} of iron used to make the tank.

**Video Solution:**

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

### NCERT Solutions for Class 9 Maths - Chapter 13 Exercise 13.8 Question 6:

**Summary:**

It is given that the hemispherical tank is made up of an iron sheet 1 cm thick. We have found that 0.06348 m^{3} of iron used to make the tank.