Question

volume of a right circular cone is 100 pi cube cm and its height is 12 cm .find its slant height and its curved surface area?

Answer 1

$volume \: = \frac{1}{3} \pi {r}^{2} h \\ \frac{1}{3} \pi \times {r}^{2} \times 12 = 100\pi \\ r = \sqrt{25} = 5 \\ \\ slant \: height \: \: \: l = \sqrt{ {r}^{2} + {h}^{2} } \\ l = \sqrt{ {5}^{2} + {12}^{2} } = 13 \\ \\ curved \: \: surface \: \: area = \pi \: r \: l \\ = \pi \times 5 \times 13 = 65\pi$