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Q.

A cylinder, a cone and a sphere are of the same radius and same height. Find the ratio of their curved surface.

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a

2: 5   : 4

b

4   : 5   : 4 

c

1 : 5   : 1

d

4   : 5   : 3

answer is D.

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Detailed Solution

Given,
Radius of the cylinder, a cone and a sphere = r.
Height of the cylinder, a cone and a sphere = h.
The respective formulas are,
Curved surface area of the cylinder =2πrh  .
Curved surface area of the cone =πrl  .
Curved surface area of the sphere =4π r 2  .
For the curved surface area of the cone, we need to find the slant height.
Slant height of the cone (l) = r 2 + h 2     ⇒ r 2 + (2r) 2    ⇒ 5 r 2    ⇒ 5 r  
So, Curved Surface area of cylinder : Curved Surface area of the cone : Curved Surface area of the sphere.
⇒   2πrh   : πrl:4π r 2   ⇒2πr(2r)   : πr( 5 r):4π r 2   ⇒4π r 2   : 5 π r 2   : 4π r 2   ⇒4   : 5   : 4
The ratio of curved surface areas of cylinder, cone and sphere of same radius and same height is 4   : 5   : 4 .
Therefore, the correct option is 4.
 
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