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.
Answers
Answered by
0
Answer:
Step-by-step explanation:
Height of cone=24
Radius=6cm
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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Answered by
1
Answer:
Height of the cone = 24 cm
Radius of base =6cm
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
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