Question

The internal and external diametres of a hemisheprical vessel are 24cm and 25cm respectively. Cost of painting 1cm sq.is Rs.0.05 . Find the total cost of painting the total hemispherical vessel.

Answer 1

Internal radius of hemispherical vessel = $\frac{24}{2}=12$ cm
Then, internal surface area of this vessel = $2\mathrm{\pi }{\left(12\right)}^2=2\times \frac{22}{7}\times 144=905.14{\mathrm{cm}}^2$
External radius of hemispherical vessel = $\frac{25}{2}=12.5$ cm
Then, its external surface area = $2\mathrm{\pi }{\left(12.5\right)}^2=2\times \frac{22}{7}\times 156.25=982.14{\mathrm{cm}}^2$
So total curved surface area of hemispherical vessel = internal surface area + external surface area = $905.14+982.14=1887.28c{m}^2$
Also area of rim = $\mathrm{\pi }\left(12.5^2-{12}^2\right)=\frac{22}{7}\times 12.25=38.5{\mathrm{cm}}^2$
Therefore total surface area of hemispherical vessel = $\left(1887.28+38.5\right)c{m}^2=1925.78c{m}^2$

So total cost of painting the total hemispherical vessel = $1925.78\times 0.05=\mathrm{Rs}.96.25$