Question

a hemispherical dome of the building is to be white washed and the total cost of white wash of dome building is rs 924 at the rate of rs 3 per m2. then find the surface area of hemisphere and also find the volume of air in the dome.

Answer 1

Total cost = ₹924

Cost of whitewash = ₹3/m²

∴ Area of dome = $\frac{total cost}{cost per m^2}$

⇒ $\frac{924}{3}$ = 308 m²

Curved surface area of hemisphere = 2πr²

⇒ 308 = 2 × $\frac{22}{7}$ × r²

⇒ 154 = $\frac{22}{7}$ × r²

⇒ 1078 = 22 × r²

⇒ 49 = r²

⇒ r = $\sqrt{49}$ = 7 m

∴ Volume of hemisphere = $\frac{2}{3}\pi r^3$

= $\frac{2}{3}$ × $\frac{22}{7}$ × 7 × 7 × 7

= $\frac{44}{3}$ × 49

= $\frac{2156}{3}$

= 718.6 m³