Question

The ratio between the radius and height of a cylinder of volume 502.4 in 2:5 .find its height.

Answer 1

$vol \: of \: cylinder \: = 502.4 \\ \pi {r}^{2} h = 502.4 \\ 3.14 \times {r}^{2} \times \binom{5}{2} r = 502.4 \\ {r}^{3} = \binom{502.4}{3.14} \times \binom{2}{5} \\ {r}^{3} = 160 \times \binom{2}{5} \\ {r}^{3} = 32 \times 2 \\ {r}^{3} = 64 \\ r = 4 \\ h = \binom{5}{2} \times r \\ h = \binom{5}{2} \times 4 \\ h \times 5 \times 2 \\ h = 10$