Question

Example 7.12 A sphere, a cylinder
and a cone (Fig. 7.20) are of the same
radius, where as cone and cylinder
are of same height. Find the ratio of
their curved surface areas.​

Answer 1

Answer:

4 : 4 : √5

Step-by-step explanation:

Radius of sphere = Radius of cone = Radius of cylinder = r

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 +  ) = √( 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