Question

The total surface area of a solid hemisphere is equal to the curved surface area of a cylinder.
The radius of the hemisphere is r cm.
The radius of the cylinder is twice the radius of the hemisphere.

Given that

volume of hemisphere : volume of cylinder = 1 : m

find the value of m.

Answer 1

Answer:

See this attachment...

Answer 2

Answer :-

→ TSA of hemisphere = CSA of cylinder

→ 3πr² = 2π(2r)h

→ 3πr² = 4πrh

→ 3r = 4h

→ h = (3r/4) .

so,

→ volume of hemisphere : volume of cylinder = 1 : m

→ (2/3)πr³ : π*(2r)²*(3r/4) = 1 : m

→ (2/3)πr³ : 3πr³ = 1 : m

→ (2/3) : 3 = 1 : m

→ (2/3) / 3 = 1/m

→ (2/3) * (1/3) = 1/m

→ (2/9) = 1/m

→ 9 = 2m

→ m = (9/2)

→ m = 4.5 (Ans.)

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