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Question
A cone of height 20 cm and radius of base 5 cm is made up of modeling clay. A child reshapes it in the form of a sphere. Find the diameter of the sphere.
Solution
Let the radius of the sphere be r.
Radius of the cone = 5 cm
Height of the cone = 20 cm
Since the cone is reshaped to form a sphere, the volumes of the sphere and the cone are equal.
`∴ 4/3pir^3=1/3pi(5cm)^2xx(20 cm)` `(∵ \text{Text of cone =}1/3 piR^2H)`
`rArr r^3=125 cm^3`
`rArr r^3=(5 cm)^3`
`rArr r^3=5 cm`
Therefore, diameter of the sphere = 2r = 2 × 5 cm = 10 cm
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