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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 total surface area of the solid in π m².
Solution:
For calculating the total surface area of the provided model, which consists of a cylinder with a hemisphere situated on top of it at one end, we must add the base area and curved surface area of the cylinder to the curved surface area of the 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
Total surface area of the solid = Base area of the cylinder + Curved surface area of the cylinder + curved surface area of the hemisphere
=π r2+2π rh + 2π r2
=π r(r+2h+2r)
= π 600(600+2×1600+2×600)
=π 600 ×(600+3200+1200)
= π 600 ×(5000)
= 3000000π cm2
= 300 π m2
Hence the total surface area of the solid is 300 π m2. 
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