Experts give the solution of this q ...

Dear Student

(i) Cost of white-washing the dome from inside = Rs 4989.60

Cost of white-washing 1 m² area = Rs 20

Therefore, CSA of the inner side of dome = $\frac{4989.6}{20} = 249.48 m^{2}$

(ii) Let the inner radius of the hemispherical dome be r.

CSA of the inner side of dome = 249.48 m²

2πr² = 249.48 m²

$\Rightarrow 2 \times \frac{22}{7} \times r^{2} = 249.48 \Rightarrow r^{2} = \frac{249.48 \times 7}{2 \times 22} = 39.69 m^{2} r = 6.3 m$

⇒ r = 6.3 m

Volume of air inside the dome = Volume of hemispherical dome

$= \frac{2}{3} {πr}^{3} = \frac{2}{3} \times \frac{22}{7} \times 6 . 3^{3}$

= 523.908 m³

= 523.9 m³ (approximately)

Therefore, the volume of air inside the dome is 523.9 m³.

Regards