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A cylinder, a hemisphere and a cone have the same base and same height. Their areas of curved surfaces are in the ratio-
Question

A cylinder, a hemisphere and a cone have the same base and same height. Their areas of curved surfaces are in the ratio-

A.

√3 : √3 : 1

B.

1 : √3 : √3

C.

√2 : 1 : √3

D.

√2 : √2 : 1

Correct option is D

Given:
All have same base radius (r) and same height (h).
Formula used:
·       Curved surface area of cylinder = 2πrh
·       Curved surface area of hemisphere = 2πr²
·       Curved surface area of cone = πrl, where l = √(r² + h²)
Solution:
Given height h = r (since same height and base)
Then,
l = √(r² + h²) = √(r² + r²) = √2 r
Now,
Cylinder : Hemisphere : Cone
= 2πrh : 2πr² : πrl
= 2πr² : 2πr² : πr(√2r)
= 2 : 2 : √2
Simplify ratio → divide by √2:
√2 : √2 : 1
Correct answer is (d) √2 : √2 : 1

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