Question

A cylinder and a cone are of the same base radius and of the same height. Find the ratio of the curved surface area of the cylinder to that of cone.

Answer 1

The ratio of the curved surface area of the cylinder to that of cone is 2h : l .

Step-by-step explanation:

Let radius of cylinder = r = radius of cone also

height of cylinder = h = height of cone

We know that,

Curved surface area of the cylinder = 2πrh Square units

And,

Curved surface area of the cone = πrl Square units

Where, l is the slant height of cone

$l=\sqrt{r^{2} +h^{2} }$

∴ The ratio of the curved surface area of the cylinder to that of cone

= 2πrh : πrl

=  2h : l or 2h : $=\sqrt{r^{2} +h^{2}}$

Hence, the ratio of the curved surface area of the cylinder to that of cone is 2h : l .