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Question
A solid metallic sphere of radius 6 cm is melted and made into a solid cylinder of height 32 cm. Find the:
(i) radius of the cylinder
(ii) curved surface area of the cylinder
Take π = 3.1
Solution
Let the radius of the sphere in γ1 and radius of cylinder is γ2 and the height of the cylinder is h.
∴ Volume of sphere = Volume of cylinder
`4/3 pi gamma_1^3 = pi gamma _2^2 h`
`⇒ 4/3 (6)^3 = gamma_2^2 xx (32) `
`⇒ 4/3 xx (36 xx 6)/8 = gamma_2^2`
`⇒ gamma_2^2 = (12xx6)/8`
`⇒gamma_2 = 3`
Radius of the cylinder is 3.
Curved surface area 2`pi gammah`
`=2 xx 22/7 xx 3 xx32 = 6.3.428 " cm"^2`
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