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ML Aggarwal Solutions Class 10 Mathematics Solutions for Mensuration Exercise 17.4 in Chapter 17 - Mensuration
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The adjoining figure represents a solid consisting of a right circular cylinder with a hemisphere at one end and a cone at the other. Their common radius is 7 cm. The height of the cylinder and the cone are each of 4 cm. Find the volume of the solid.
Solution:
Since the given solid is a combination of a cone, cylinder, and hemisphere, we must sum the volumes of the cone, cylinder, and hemisphere to determine its volume.
Given common radius, r = 7 cm
Height of the cone, h = 4 cm
Height of the cylinder, H = 4 cm
Volume of the solid = Volume of the cone + Volume of the cylinder + Volume of the hemisphere
= (1/3)π r2h +π r2H + (2/3) π r3
= π r2((h/3) + H + (2r/3))
= (22/7)×72×((4/3)+4+(2×7)/3)
= (22×7×((4+12+14)/3)
= 22×7×30/3
= 1540 cm3
Hence the volume of the solid is 1540 cm3. 
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