The radius of the internal and external surfaces of a hollow spherical shell are 3 cm and 5 cm respectively!

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asked Mar 19 in Class X Maths by priya12 (-11,081 points)

The radius of the internal and external surfaces of a hollow spherical shell are 3 cm and 5 cm respectively! If it is melted and recast into a solid cylinder of height 8/3 cm, find the diameter of the cylinder.

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answered Mar 19 by muskan15 (-1,962 points)

Internal radius of hollow spherical shell

(r1) = 3 cm

External radius of hollow spherical = (r2) = 5 cm

Volume of hollow spherical = 4/3π(r23 – r13)

= 4/3π[(5)3 – (3)3]

= 4/3π(125 – 27)

= (4π × 98)/3 = 392π/3 cm3

Volume of cylinder  = Volume of hollow sphere

8πr2/3 = 392π/3

r2 = 392π × 3/8π × 3

r2 = 49

r = √49

r = 7 cm

The diameter of cylinder = 2r = 2 × 7 = 14 cm

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