A cone of height 24 and radius and base 6 cm is made up of modelling clay .A child reshapes it in the form of a sphere.Find the radius of sphere and surface area of sphere
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7
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Height of cone=24
Radius=6cm
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Vol of cone=1/3πr^2h
=1/3π*6^2*24
=1/3π×36×24
= 288πcm^3
Let,
The vol of sphere = 4/3π^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=
]
Therefore , The radius if circle is 6cm
]
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 sphere = 4/3π^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=
]
Therefore , The radius if circle is 6cm
TRISHNADEVI:
surface area of the sphere also be calculate
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