Question

The radius and height of a right circular cone are in the ratio 3:4 and its volume is 96pie cm cube what is the lsa

Answer 1

$volume \: of \: cone \: = \frac{1}{3} \times \pi \times {r}^{2} \times h = 96\pi \: {cm}^{3} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{1}{3} \times {r}^{2} \times h = 96 \: {cm}^{3} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = {r}^{2} \times h = 96 \times 3 \\ let \: the \: radius \: and \: height \: be \: 3x \: and \: 4x \: respectively \\ substituting \: the \: values \: we \: get \\ {r}^{2} \times h = 96 \times 3 \\ 9 {x}^{2} \times 4x = 96 \times 3 \\ 36 {x}^{3} = 288 \\ {x}^{3} = 8 \\ x = 2 \\ lsa = \: \pi \times r \times l \\ l = \sqrt{ {r}^{2} + {h}^{2} } \\ \: \: \: \: = \sqrt{ {6}^{2} + {8}^{2} } \\ \: \: \: \: \: = 10 \\ so \: lsa = \pi \times 6 \times 10 \\ \: \: \: \: \: = 60\pi \: {cm}^{2}$