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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 shows a model of a solid consisting of a cylinder surmounted by a hemisphere at one end. If the model is drawn to a scale of 1 : 200, find the volume of the solid in π litres.
Solution:
Here, the model is a combination of a cylinder with a hemisphere at one end, therefore to calculate its volume, we must sum the volumes of the cylinder and hemisphere.
Given height of the cylinder, h = 8 cm
Radius of the cylinder, r = 3 cm
Radius of hemisphere , r = 3 cm
Scale = 1:200
Hence actual radius, r = 200×3 = 600
Actual height, h = 200×8 = 1600
Volume of the solid = Volume of the cylinder + Volume of the hemisphere
= π r2h + (2/3) π r3
=π r2(h+ (2/3)r)
= π 6002(1600+ (2/3)×600)
= π 360000 (1600+400)
=π 360000 ×2000
= 720000000 π cm3
= 720π m3
= 720000 litres [1 m3 = 1000 litres]
Hence the volume of the solid is 720000 π litres. 
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