Question

the total surface area of a solid cylinder is 231 cn² and its curved surface area is ⅔ of the total surface are.Find the volume of the cylinder.

Answer 1

$total \: surface \: area \: of \: cylinder \: \\ = 231 {cm}^{2} \\ its \: curved \: surface \: area \: = 2\pi.rh \\ total \: surface \: area \: = \\ 2\pi.rh + 2\pi. {r}^{2} \\ \\ 2\pi.rh + 2\pi. {r}^{2} = 231 \\ curved \: surface \: is \: \frac{2}{3} of \: \\ total \: surface \\ therefore \\ \\ 2\pi.rh = \frac{2}{3} \times 231 \\ 2\pi.rh = 154 \\ substitute \: value \: from \: \\ equation \: 2 \: in1 \: we \: get \: \\ 154 + 2\pi. {r}^{2} = 231 \\ 2\pi. {r}^{2} = 231 - 154 \\ 2\pi. {r}^{2} = 77 \\ 2 \times \frac{22}{7} \times {r}^{2} = 77 \\ {r}^{2} = 77 \times \frac{7}{44} \\ {r}^{2} = \frac{539}{44} \\ {r}^{2} = 12.25 \\ r = \sqrt{12.25} \\ r = 3.5 \\ then \\ \\ 2 \times \frac{22}{7} \times 3.5 \times h = 154 \\ (44 \times 3.5) \frac{h}{7} = 154 \\ 22h = 154 \\ h = \frac{154}{22} \\ h = 7cm \\ \\ so \: height = 7cm \: and \\ \: volume \: = 3.5cm$