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Question
A metallic sphere of radius 4.2 cm is melted and recast into the shape of a cylinder of radius 6 cm. Find the height of the cylinder.
Solution
Radius (r1) of hemisphere = 4.2 cm
Radius (r2) of cylinder = 6 cm
Let the height of the cylinder be h.
The object formed by recasting the hemisphere will be the same in volume.
Volume of sphere = Volume of cylinder
`4/3 pir_1^3 = pir_2^2h`
`4/3pi(4.2)^3 = pi(6)^2h`
`4/3 xx (4.2xx4.2xx4.2)/36 = h`
h = (1.4)3 = 2.74 cm
Hence, the height of the cylinder so formed will be 2.74 cm.
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