SSC CPO SI and ASI 2014 Paper

Question : 129 of 200

Marks: +1, -0

A hollow sphere of internal and external diameters 6 cm and 10 cm, respectively, is melted into a right circular cone of diameter 8 cm. The height of the cone is

22.5 cm
23.5 cm
24.5 cm
25.5 cm

Validate

Solution:

(3) Let h be the height of the cone.
Since, volume of hollow sphere will be equal to the volume of cone so,

{4}/{3} \π(R^{3}-r^{3} )= {1}/{3} \π× r^{2}× h

{4}/{3} \π(5^{3}-3^{3} )= {1}/{3} \π 4^{2}× h

⇒ h= {98}/{4}=24.5 {cm}

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