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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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5

: 4

4

5

: 4

1 :

5

: 1

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

= 2 π r h

.
Curved surface area of the cone

= π r l

.
Curved surface area of the sphere

= 4 π 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 + (2 r) 2

⇒ 5 r 2

⇒ 5 r

So, Curved Surface area of cylinder : Curved Surface area of the cone : Curved Surface area of the sphere.

⇒

2 π r h

π r l : 4 π r 2

⇒ 2 π r (2 r)

π r (5 r) : 4 π r 2

⇒ 4 π r 2

5 π r 2

4 π 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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