Question

A cylindrical vessel, without lid, has to be tin-coated on its both sides. If the radius of the base is 70 cm and its height is 1.4 m, calculate the cost of tin-coating at the rate of Rs 3.50 per 1000 cm².

Answer 1

$$\begin{gathered} \mathrm{Let}r\mathrm{cm}\mathrm{and}\mathit{}h\mathit{}\mathrm{cm}\mathrm{be}\mathrm{the}\mathrm{radius}\mathrm{of}\mathrm{the}\mathrm{cylindrical}\mathrm{vessel}. \\ \mathrm{Given}: \\ \mathrm{Radius},r=70\mathrm{cm} \\ \mathrm{Height},h=1.4\mathrm{m}=140\mathrm{cm} \\ \mathrm{Rate}\mathrm{of}\mathrm{tin}-\mathrm{plating}=\mathrm{Rs}3.50\mathrm{per}1000\mathrm{square}\mathrm{centimetre} \\ \mathrm{Cost}\mathrm{of}\mathrm{tin}-\mathrm{plating}\mathrm{the}\mathrm{cylindrical}\mathrm{vessel}\mathrm{on}\mathrm{both}\mathrm{the}\mathrm{surfaces}(\mathrm{inner}\mathrm{and}\mathrm{outer}): \\ \mathrm{Total}\mathrm{suface}\mathrm{area}\mathrm{of}\mathrm{a}\mathrm{vessel}=\mathrm{Area}\mathrm{of}\mathrm{the}\mathrm{inner}\mathrm{and}\mathrm{the}\mathrm{outer}\mathrm{side}\mathrm{of}\mathrm{the}\mathrm{base}+\mathrm{Area}\mathrm{of}\mathrm{the}\mathrm{inner}\mathrm{and}\mathrm{the}\mathrm{outer}\mathrm{curved}\mathrm{surface} \\ =2\left(\mathrm{\pi }{r}^2+2\mathrm{\pi }rh\right) \\ =2\mathrm{\pi }r\left(\mathrm{r}+2h\right) \\ =2\times \frac{22}{7}\times 70\times \left(70+2\times 140\right) \\ =44\times 10\times 350 \\ =154000{\mathrm{cm}}^2 \\ \mathrm{Cost}\mathrm{of}\mathrm{painting}\mathrm{at}\mathrm{the}\mathrm{rate}\mathrm{of}\mathrm{Rs}3.50\mathrm{per}1000{\mathrm{cm}}^2=154000\times \frac{3.50}{1000}=\mathrm{Rs}539 \\ \mathrm{Therefore},\mathrm{cost}\mathrm{of}\mathrm{painting}\mathrm{is}\mathrm{Rs}539. \end{gathered}$$