Question

# The ratio of the curved surface area to the total surface area of a right circular cylinder is 1 : 3. Find the volume of the cylinder if its total surface area is 1848 cm2.

Open in App
Solution

## $\mathrm{Let}\mathrm{the}\mathrm{radius}\mathrm{of}\mathrm{the}\mathrm{cylinder}\mathrm{be}r\mathrm{and}\mathrm{its}\mathrm{height}\mathrm{be}h.\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\mathrm{As},\phantom{\rule{0ex}{0ex}}\frac{\mathrm{CSA}\mathrm{of}\mathrm{the}\mathrm{cylinder}}{\mathrm{TSA}\mathrm{of}\mathrm{the}\mathrm{cylinder}}=\frac{1}{3}\phantom{\rule{0ex}{0ex}}⇒\mathrm{CSA}\mathrm{of}\mathrm{the}\mathrm{cylinder}=\frac{1}{3}×\mathrm{TSA}\mathrm{of}\mathrm{the}\mathrm{cylinder}\phantom{\rule{0ex}{0ex}}⇒\mathrm{CSA}\mathrm{of}\mathrm{the}\mathrm{cylinder}=\frac{1}{3}×1848\phantom{\rule{0ex}{0ex}}⇒\mathrm{CSA}\mathrm{of}\mathrm{the}\mathrm{cylinder}=616{\mathrm{cm}}^{2}\phantom{\rule{0ex}{0ex}}⇒2\mathrm{\pi }rh=616.....\left(\mathrm{i}\right)\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\mathrm{Also},\phantom{\rule{0ex}{0ex}}\mathrm{TSA}\mathrm{of}\mathrm{the}\mathrm{cylinder}=1848{\mathrm{cm}}^{2}\phantom{\rule{0ex}{0ex}}⇒2\mathrm{\pi rh}+2\mathrm{\pi }{r}^{2}=1848\phantom{\rule{0ex}{0ex}}⇒616+2\mathrm{\pi }{r}^{2}=1848\left[\mathrm{Using}\left(\mathrm{i}\right)\right]\phantom{\rule{0ex}{0ex}}⇒2\mathrm{\pi }{r}^{2}=1848-616\phantom{\rule{0ex}{0ex}}⇒2×\frac{22}{7}×{r}^{2}=1232\phantom{\rule{0ex}{0ex}}⇒{r}^{2}=\frac{1232×7}{2×22}\phantom{\rule{0ex}{0ex}}⇒{r}^{2}=196\phantom{\rule{0ex}{0ex}}⇒r=\sqrt{196}\phantom{\rule{0ex}{0ex}}⇒r=14\mathrm{cm}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\mathrm{Substituting}r=14\mathrm{cm}\mathrm{in}\left(\mathrm{i}\right),\mathrm{we}\mathrm{get}\phantom{\rule{0ex}{0ex}}2\mathrm{\pi }×14×h=616\phantom{\rule{0ex}{0ex}}⇒2×\frac{22}{7}×14×h=616\phantom{\rule{0ex}{0ex}}⇒88h=616\phantom{\rule{0ex}{0ex}}⇒h=\frac{616}{8}\phantom{\rule{0ex}{0ex}}⇒h=7\mathrm{cm}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\mathrm{Now},\phantom{\rule{0ex}{0ex}}\mathrm{Volume}\mathrm{of}\mathrm{the}\mathrm{cylinder}=\mathrm{\pi }{r}^{2}h\phantom{\rule{0ex}{0ex}}=\frac{22}{7}×14×14×7\phantom{\rule{0ex}{0ex}}=4312{\mathrm{cm}}^{3}$ So, the volume of the cylinder is 4312 cm3.

Suggest Corrections
2