Q2 of 227 Page 897

A cone of height 20 cm and radius of base 5 cm is made up of modelling clay. A child reshapes it in the form of a sphere. Find the diameter of the sphere.

We have,


The radius of the cone (r) = 5cm and


The height of the cone (h) = 20cm


Let the radius of the sphere be R;


As,


Volume of sphere = Volume of cone


⇒ πR3 = πr2h


⇒ 4R3 = 5 × 5 × 20


⇒ R3 = = 125 cm


⇒ R = 5 cm


Diameter of the sphere = 2R = 2 x 5 = 10 cm


So, the diameter of the sphere is 10 cm


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