Question

a sphere a cylinder and a cone are of same radius and same height the ratio of the curved surface area is

Answer 1

this is the answer of the following questions

Answer 2

Given,

A sphere, a cylinder and a cone are of same radius and same height.

To find out,

The ratio of the curved surface area.

Solution:

Let "r" be the common radius of a sphere, cone and

cylinder.

Height of sphere = its diameter = 2r.

Then, the height of the cone = height of cylinder = height of sphere = 2r

$The \: slant \: height \: of \: cone \: (l) \: = \sqrt{ {r}^{2} + {h}^{2} } \\ \\ \sqrt{ {r}^{2} + {2r}^{2} } \\ \\ = \sqrt{5} r$

$Curved \: surface \: area \: of \: sphere \: = 4 \pi \: {r}^{2} \\ \\ </p><p>Curved \: surface \: area \: of \: cylinder \: = 2 \pi \: rh = 2 \pi \: r \: \times 2r = 4 \pi \: {r}^{2} \\ \\ </p><p>Curved \: surface \: area \: of \: cone \: = \pi \: r \: l = \pi \: r \: \times \sqrt{5} r = \sqrt{5} \pi \: {r}^{2}$

Therefore the ratio of curved surface area is

$4 \pi \: {r}^{2} : \: 4 \pi \: {r}^{2} : \: \sqrt{5} \pi \: {r}^{2} \\ \\ 4: 4: \sqrt{5}$