## A cone of height 24 em and radius of base 6 cm is made up of modelling clay, A child moulds it in the form of a sphere. Find

Question

A cone of height 24 em and radius of
base 6 cm is made up of modelling clay,
A child moulds it in the form of a
sphere. Find the radius of the sphere.​

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1 month 2021-08-14T00:32:46+00:00 2 Answers 0 views 0

Height of the cone = 24 cm

So Volume of the cone = (1/3) π r²h cm³

= (1/3) π×6² × 24 cm³

= 8π×36 cm³

= 288π cm³

Let r be the radius of the sphere

So the vol of sphere = ( 4/3) π r³

Volume of sphere=Volume of cone

So

( 4/3) πr³ =288π

r³ =288 × 3/4

r³ = 216

r = 6

So the required radius of the sphere is 6 cm

Step-by-step explanation:

Height of cone=24

Vol of cone=1/3πr^2h

=1/3π*6^2*24

=1/3π*36*24

=288πcm^3

Let the vol of sphere4/3π^3

Vol of sphere=Vol of cone

4/3π^3=288π

4/3^3=288

r^3=288*3/4

r^3=72*3

r^3=8*9*3

r^3=(2*2*2*3*3*3)

r=(2*2*2*3*3*3)1/3

r=(2*2*2)1/3 * (3*3*3)1/3

r=(2^3)1/3 * (3^3)1/3

r=2*3

r=6cm

Therefore the radius if circle is 6cm

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