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Question
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.
Solution
We have,
the base radius of the cone, r=5 cm and
the height of the cone, h = 20 cm
Let the radius of the sphere be R.
As,
Volume of sphere = Volume of cone
`rArr 4/3piR^3 = 1/3pir^2h`
`rArr R^3 = (pir^2hxx3)/(3xx4pi)`
`rArr R^3 = (r^2h)/4`
`rArr R^3 = (5xx5xx20)/4`
`rArr R^3 = 125`
`rArr R = root(3)(125)`
⇒ Diameter of the sphere = 2R= 2×5 = 10 cm
So, the diameter of the sphere is 10 cm.
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