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ML Aggarwal Solutions Class 10 Mathematics Solutions for Mensuration Exercise 17.5 in Chapter 17 - Mensuration
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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.
Solution:
When we convert one solid shape to another, its volume remains the same, no matter how different the new shape is. So this is the case of sphere to cylinder conversion.
Given radius of the sphere, r = 6 cm
Volume of the sphere = (4/3)π r3
= (4/3)π ×63
= 288π 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 = π (R2-r2)h
Since sphere is melted and changed into a hollow cylinder, their volumes remain same.
π (R2-r2)h = 288π
π (42-r2)×72 = 288π
(42-r2) = 288/72
(42-r2) = 4
16-r2 = 4
r2 = 16-4
r2 = 12
r = 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.
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