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Question

A hemisphere of radius 21cm, made up of iron is melted and moulded to form a cone of height 21 cm. What is the ratio of the curved surface area of the cone to that of the hemisphere?

A

1:2

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B

23:5

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C

22:3

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D

3:2

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Solution

The correct option is D √3:√2 Given, radius of hemisphere and height of cone = 21 cm Let r be the radius of the cone. Volume of the hemisphere =23π(21)3=6174π cm3 The hemisphere is molded into a cone, hence, the volume of cone will be equal to the volume of the hemisphere. 13π×r2×21=6174πr=21√2 cm Slant height of the cone, l2=h2+r2 =212+(2).212⇒l=21√3 cm Curved surface area of the cone =πrl=π(21√2)(21√3)=π(21)2√2.√3 Curved surface area of the hemisphere =2πr2=2π(21)2 Ratio of the curved surface areas of cone to hemisphere = π(21)2√2.√32π(21)2 =√3:√2

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