Question

Cost of painting the Total Surface Area (T.S.A.) of cylinder at the rate of rupees 5/m²is 1540. The height of cylinder is 3 times its radius. Find the volume of cylinder.

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{r}\mathrm{be}\mathrm{the}\mathrm{radius}\mathrm{of}\mathrm{base}\mathrm{and}\mathrm{h}\mathrm{be}\mathrm{the}\mathrm{height}\mathrm{of}\mathrm{cylinder}. \\ \mathrm{Now},\mathrm{h}=3\mathrm{r} \\ \mathrm{Now},\mathrm{area}\mathrm{painted}\mathrm{for}\mathrm{Rs}5=1{\mathrm{m}}^2 \\ \mathrm{So},\mathrm{area}\mathrm{painted}\mathrm{for}\mathrm{Rs}1540=\left(\frac{1540}{5}\right)=308{\mathrm{m}}^2 \\ \mathrm{Now},\mathrm{TSA}\mathrm{of}\mathrm{cylinder}=308{\mathrm{m}}^2 \\ \Rightarrow 2\mathrm{\pi r}\left(\mathrm{h}+\mathrm{r}\right)=308 \\ \Rightarrow 2\times \frac{22}{7}\times \mathrm{r}\left(3\mathrm{r}+\mathrm{r}\right)=308 \\ \Rightarrow \frac{44}{7}\times 4{\mathrm{r}}^2=308 \\ \Rightarrow {\mathrm{r}}^2=\frac{49}{4} \\ \Rightarrow \mathrm{r}=\frac{7}{2}\mathrm{m}=3.5\mathrm{m} \\ \mathrm{Now},\mathrm{h}=3\mathrm{r}=\frac{21}{2}\mathrm{m}=10.5\mathrm{m} \\ \mathrm{Volume}\mathrm{of}\mathrm{cylinder}={\mathrm{\pi r}}^2\mathrm{h}=\frac{22}{7}\times \frac{7}{2}\times \frac{7}{2}\times \frac{21}{2}=404.25{\mathrm{m}}^3 \end{gathered}$$