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# A solid sphere of radius 6 cm is melted into a hollow cylinder of uniform thickness. If the external radius of the base of the cylinder is 4 cm and height is 72 cm, find the uniform thickness of the cylinder.

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This question is Based on Mensuration Chapter of M.L Aggarwal book for ICSE BOARD for class 10.
In this question a solid sphere radius is given it is melted into a hollow cylinder of uniform thickness.
If the external radius of the base of the cylinder and height is given,
Then find the uniform thickness of the cylinder.
This is the Question Number 11, Exercise 17.5 of M.L Aggarwal.

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1. Given radius of the sphere, r = 6 cm

Volume of the sphereÂ = (4/3)r3

= (4/3)Ã—63

= 288 cm3

Let r be the internal radius of the hollow cylinder.

External radius of the hollow cylinder, R = 4 cm

Height of hollow cylinder, h = 72 cm

Volume of hollow cylinder = (R2-r2)h

Since sphere is melted and changed into a hollow cylinder, their volumes remain same.

(R2-r2)h = 288

(42-r2)Ã—72 = 288

(42-r2) = 288/72

(42-r2) = 4

16-r2Â = 4

r2Â = 16-4

r2Â = 12

r = 2âˆš3 cm

So thickness = R-r = 4-2âˆš3

= 4- 3.464

= 0.536 cm

= 0.54 cm (approx)

Hence the thickness of the cylinder is 0.54 cm.

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