Question

A cylindrical vessel open at the top has diameter 20 cm and height 14 cm. Find the cost of tin-plating it on the inside at the rate of 50 paise per hundred square centimetre.

Answer 1

$$\begin{gathered} \mathrm{Given}: \\ \mathrm{Diameter},d=20\mathrm{cm} \\ \mathrm{Radius},r=10\mathrm{cm} \\ \mathrm{Height},\mathit{}h=14\mathrm{cm} \\ \mathrm{Area}\mathrm{inside}\mathrm{the}\mathrm{cylindrical}\mathrm{vessel}\mathrm{that}\mathrm{is}\mathrm{to}\mathrm{be}\mathrm{tin}-\mathrm{plated}=S \\ S=2\mathrm{\pi }rh+\mathrm{\pi }{r}^2 \\ =2\mathrm{\pi }\times 10\times 14+\pi \times {10}^2 \\ =280\mathrm{\pi }+100\mathrm{\pi } \\ =380\times \frac{22}{7}{\mathrm{cm}}^2 \\ =\frac{8360}{7}{\mathrm{cm}}^2 \\ \mathrm{According}\mathrm{to}\mathrm{question}: \\ \mathrm{Cost}\mathrm{per}100{\mathrm{cm}}^2=50\mathrm{paise} \\ \mathrm{Cost}\mathrm{per}{\mathrm{cm}}^2=\mathrm{Rs}0.005 \\ \mathrm{Cost}\mathrm{of}\mathrm{tin}-\mathrm{plating}\mathrm{the}\mathrm{area}\mathrm{inside}\mathrm{the}\mathrm{cylindrical}\mathrm{vessel}=Rs0.005\times \frac{8360}{7} \\ =\mathrm{Rs}\frac{41.8}{7}=\mathrm{Rs}5.97 \end{gathered}$$