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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=212 cm

Slant height of the cone, l2=h2+r2 =212+(2).212l=213 cm

Curved surface area of the cone =πrl=π(212)(213)=π(21)22.3

Curved surface area of the hemisphere =2πr2=2π(21)2

Ratio of the curved surface areas of cone to hemisphere = π(21)22.32π(21)2

=3:2


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