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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. - Mathematics

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Sum

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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Solution

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

Concept: Surface Area of a Combination of Solids
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