The dome of the building where people live is in the shape of hemisphere of radius 7 m . Eleven children decided to help the old age people by collecting money for white washing the dome . If white washing cost ₹2per sq m . How much would each children pay ? Also find the volume of air inside the dome . What values are depicted here

Answer :

Given radius of hemisphere shaped building  =  7 m
And
We want to paint that building , So , we paint only its curved surface area .
And
We know Curved surface area of hemisphere  = $2 \mathrm{\pi } {\mathrm{r}}^2$
So,
Curved surface area of hemispherical building  = $2 \times \frac{22}{7}\times 7\times 7 = 2 \times 22 \times 7 = 308 {\mathrm{m}}^2$
And rate of white wash is Rs 2 / m² , So
Cost of painting the building  =  308 $\times$ 2  =  Rs. 616
And

There are eleven children who are collect that money , So

Total money paid by each children  = $\frac{616}{11}$ =  Rs . 56                               ( Ans )
And
We know Volume of hemisphere  = $\frac{2 \mathrm{\pi } {\mathrm{r}}^3}{3}$
So,
Volume of hemispherical building  =  $\frac{2\times {\displaystyle \frac{22}{7}}\times 7 \times 7\times 7}{3} = \frac{2 \times {\displaystyle 22} \times 7\times 7}{3} = \frac{2156}{3} = \mathbf{718}\mathbf{.}\mathbf{67}\mathbf{ }{\mathit{m}}^{\mathbf{3}}\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{(}\mathbf{ }\mathit{A}\mathit{n}\mathit{s}\mathbf{ }\mathbf{)}$

By doing show they depicts their helping nature towards old people .