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

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This is the important problem for cbse board exam last time in 2011 this problem was asked. Problem number 2 in exercise 17B from RS Aggarwal book, chapter volume and surface area of solid.

Given data

The base radius of the cone, r = 5 cm

the height of the cone, h = 20 cm

Let the radius of the sphere be R.

Volume of sphere = Volume of cone

[ 4/3 ] πR³ = [ 1/3 ]πr²h

R³ = [πr²h*3] / 3*4π

R³ = ( [22/7] * 5² * 20 * 3 ) / 3 * 4 * [22/7]

R³ = 125

R = 5

∴ the diameter of the sphere is 10 cm.