Question

A cone hemisphere and cylinder stand on the same base and have equal hight find the ratio of their volume and curved surface area

Answer 1

Volume of cone=1/3pie r2 h
Hemisphere=2/3pie r3
Volume(c). 1/3?×22/7×r×r×r
---------------. =
Volume (h). 1/3×22/7×r×r×r
=1:1

Answer 2

$they \: have \: equal \:base \: and \: height \\ so \: h = r \\ v1 = \frac{1}{3}\pi {r}^{2}h = \frac{1}{3} \pi {r}^{2} r = \frac{1}{3}\pi {r}^{3} \\ v2 = \frac{2}{3} \pi {r}^{3} \\ v3 = \pi {r}^{2} h = \pi {r}^{3} \\ v1: \: v2 :\: v3 = 1:2:3 \\ s1 = \pi \: rl = \pi \: r \sqrt{ {r}^{2} + {h}^{2} } = \pi \: r \sqrt{ {r}^{2} + {r}^{2} } = \sqrt{2} \pi {r}^{2} \\ s2 = 2\pi {r}^{2} \\ s3 = 2\pi \: rh = 2\pi {r}^{2} \\ s1:s2:s3 = 1:2:2$