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प्रश्न
A cone of height 24 cm and radius of base 6 cm is made up of modelling clay. A child reshapes it in the form of a sphere. Find the radius of the sphere and hence find the surface area of this sphere.
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उत्तर
A cone has been reshaped in the sphere
Height of cone is 24 cm and the radius of the base is 6 cm
Volume of sphere = volume of cone
Volume of cone = `1/3`πr2h
Plugging the values in the formula we get
volume of cone = `1/3`π(6)224 = 288π cm3
Let the radius of sphere be r
Volume of sphere = `4/3`πr3
Since, the volume of cone = volume of sphere
Volume of sphere = 288π cm3
So,
288π = `4/3` πr3
⇒ 288 = `4/3`r3
⇒ r3 = 216
⇒ r = 6 cm
Hence, radius of reshaped sphere is 6 cm
Now, surface area of sphere = 4πr2
= 4π(6)2
= `144 × 22/7`
= 452.5 cm2
Therefore, surface area of sphere is 452.57 cm2
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