Question

A hollow hemispherical vessel has internal and external radius are $42cm$ and $43cm$ respectively. If cost of polishing the surface it, is $7$ paise per square cm, then find the cost of polishing the surface.

Answer 1

Internal radius of spherical vessel $=42$ cm

External radius of hemispherical vessel $=43$ cm

Total surface area to be painted

$=$ External curved surface + Internal curved surface + Area of ring

Curved surface area of hollow hemisphere $=2\pi r_1^2+2\pi r_2^2+\pi (r_2-r_1{)}^2$

where $r_2=43cm$ and $r_1=42cm$

$\therefore$ area $=$ $\pi (2\times {42}^2+2\times {43}^2+1^2)$

$=22,704.290c{m}^2$

$\therefore cost=7\times 22,704.290=158,930.46paisa$