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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# 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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Given radius of the sphere, r = 6 cmVolume of the sphere= (4/3)r^{3}= (4/3)×6

^{3}= 288 cm

^{3}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 = (R

^{2}-r^{2})hSince sphere is melted and changed into a hollow cylinder, their volumes remain same.

(R

^{2}-r^{2})h = 288(4

^{2}-r^{2})×72 = 288(4

^{2}-r^{2}) = 288/72(4

^{2}-r^{2}) = 416-r

^{2}= 4r

^{2}= 16-4r

^{2}= 12r = 2√3 cm

So thickness = R-r = 4-2√3

= 4- 3.464

= 0.536 cm

= 0.54 cm (approx)

Hence the thickness of the cylinder is 0.54 cm.