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ML Aggarwal Solutions Class 10 Mathematics Solutions for Mensuration Exercise 17.5 in Chapter 17 - Mensuration
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Find the number of metallic circular discs with 1.5 cm base diameter and height 0.2 cm to be melted to form a circular cylinder of height 10 cm and diameter 4.5 cm.
Solution:
No matter how different the new shape is, when we change one solid shape into another, its volume stays the same. In fact, the volume of the cylinder is equal to the sum of the volumes of the smaller circular metallic discs that result from melting one cylinder.
Given height of the circular cylinder, h = 10 cm
Diameter of circular cylinder = 4.5 cm
So radius, r = 4.5/2 = 2.25 cm
Volume of circular cylinder =π r2h
= π x2.252×10 = 50.625π cm3
Base diameter of circular disc = 1.5 cm
So radius, r = 1.5/2 = 0.75 cm
Height of the circular disc, h = 0.2 cm
Volume of circular disc = π r2h
= π x 0.752 ×0.2
= 0.1125π cm3
Number of circular discs made from cylinder = 50.625π /0.1125π = 450
Hence the number of circular discs made from cylinder is 450.
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