Question

A Sphere, a Cylinder and a Cone are of the same radius and same height. Then ratio of their curved surface area is ________

Answer 1

Curved surface area of sphere is $4\pi r^2$

Curved surface area of cylinder is $2\pi rh$

Curved surface area of cone is $\pi rl=\pi r\sqrt{r^2+h^2}$

Ratio will be $4\pi r^2:2\pi rh:\pi r\sqrt{r^2+h^2}=4r:2h:\sqrt{r^2+h^2}$
Given, height is same for all the solids, then $h=2r$(as height of the sphere is $2r$)

Then ratio becomes $4r:2\left(2r\right):\sqrt{r^2+4r^2}$
$=4:4:\sqrt{5}$