A dome of a building is in the form of a hemisphere.From inside it was washed at the cost of Rs. 498.96 .If the cost of white washing is Rs. 2.00 per square metre,find the inside surface area of the dome and volume of the air inside the dome.

Let the radius of the dome be r m.

Then area of washing = 2 * pie * r^{2}

Rate of washing = Rs. 2 per m^{2}

Cost of washing = 2 * ( 2 * pie * r^{2})

But, it is given to be Rs. 498.96

So, 2 ( 2 * pie * r^{2} ) = 498.96

or, r = 6.3 m

Inside surface area of the dome = 2 * pie * r^{2} = 2 * 22/7 * 6.3 * 6.3 = 249.48m^{2}

Volume of air inside it = 2/3 * pie * r^{3}

2/3 * 22/7 * 6.3 * 6.3 * 6.3 = 523.908 m^{3} = 524m^{3} ( approx.)

Hope it works !!