Question

A dome of a building is in the form of a hemisphere. From inside it was white washed at the cost of ₹ 498.96 . If the cost of white washing is ₹ 2 per square metre, then find the
i) Inside surface area of the dome
ii)Volume of the air inside the dome.

Answer 1

Solution:-

Given:-

Cost of 1m² of Dome = ₹2

Cost of 1m² of Dome = ₹2

Total Cost of painting the Dome = ₹498.96

Hence,

Surface Area of Dome = Total Cost of Painting/ Cost of 1m²

=> Surface Area = 498.96/2

=> Surface Area of the Dome = 249.48 m².

=> 2 πr² = 249.48

=> r² = (249.48 × 7)/2×22

=> r² = 39.96

=> r = √39.96

=> r = 6.32 m

Now,

Volume of Air Inside the Dome = Volume of Hemisphere

=> Volume of Hemisphere = 2πr³/3

=> (2 × 22× 6.32 × 6.32 × 6.32)/3×2

=> 22 × 2.16 × 6.32 × 6.32

=> 1898.06 m³

Hence,

Volume of Air Inside the Dome is 1898.06 m³.