Question

Example 7.12 A sphere, a cylinder
and a cone are of the same
radius, where as cone and cylinder
are of same height. Find the ratio of
their curved surface areas.​

Answer 1

Since, the height of a sphere is the diameter, the cone and cylinder have height 2r.

Then Curved surface area of Sphere= 4πr²

Curved surface area of cylinder = 2πr(2r) = 4πr²

Curved surface area of cone = πrl

where, l = √(r2 + h2 ) = √( r2 + (2r)2) = √(5r2) = r√5

⇒ Curved surface area of cone = π√5r2

Now,

Ratio of CSA 's a sphere ,cylinder and a cone = 4πr2:2πrh : πrl

= 4πr2:4πr2 : πr2√5

= 4 : 4 : √5