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(R3−r3) =43π(43−23) =43π(64−8) =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㎝