Question

A hemisphere and a cone have equal bases. If their heights are also equal, then what is the ratio of their curved surfaces?

Answer 1

Answer:

The Ratio of the curved surface area of hemisphere and cone = √2 : 1

Step-by-step explanation:

Given :

Base of a cone and hemisphere are equal then their Radius are also equal.

Radius and heights of the hemisphere and cone are same.

Let the radius of the hemisphere = radius of the cone = r

Height of the cone =  radius of the hemisphere =  r

Slant height of a cone, l = √r² + h²

l = √r² + r²

l = √2r²

l = r√2 ………….(1)

Curved surface area of hemisphere  (S1) / Curved surface area of cone (S2) = 2πr² /πrl

S1/S2 = 2πr² /πrl

S1/S2 = 2r/l

S1/S2 = 2r/r√2

[From eq 1]

S1/S2 = 2/√2

S1/S2 = (2 × √2 )/(√2 × √2)

[On rationalising the denominator]

S1/S2 = 2√2/2

S1/S2 = √2/1

S1 : S2 = √2 : 1

Ratio of the curved surface area of hemisphere and cone = √2 : 1

Hence, the Ratio of the curved surface area of hemisphere and cone = √2 : 1

HOPE THIS ANSWER WILL HELP YOU…..

Answer 2

Step-by-step explanation:

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