AP ICET 2014

Question 104

A cone of height 24 cm and radius of its base 6 cm is made up of clay. If that clay is reshaped in the form of a sphere, then the diameter of that sphere (in cms) is

Solution

The volume of the clay available remains constant.
Hence, equating the volumes of the cone and the sphere:
$$\frac{1}{3}\pi\ \cdot6^2\cdot24=\frac{4}{3}\pi\ \cdot R^3$$

Solving this, we get R = 6, and hence, diameter = 12. 


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