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Question

a hollow sphere of external and internal diameters 8cm and 4cm respectively is melted into a cone of base diameter 8cm them the height of the cone is:

A
14cm
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B
18cn
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C
20cm
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D
28cm
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Solution

The correct option is B 14cm
Volume of the hollow sphere=43π(R3r3)
=43π(4323)
=43π(648)
=43π56
Diameter of the cone (d1)=8
Radius of the cone(r1)=8/2=4
Let the height of the cone be 4
Volume of the cone=13π(r1)2h
=13×π×42×h=16πh3
Volume of the cone=volume of the hollow sphere
16πh3=43π(56)
h=14

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