# ML Aggarwal Solutions Class 10 Mathematics Solutions for Mensuration Exercise 17.4 in Chapter 17 - Mensuration

Question 24 Mensuration Exercise 17.4

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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