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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 (i) the total surface area of the solid in pi (π) m square. (ii) the volume of the solid in pi (π) litres.

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M.L Aggarwal book Important Question of class 10 chapter Based on Mensuration for ICSE BOARD.
This 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 and the volume of the solid in π litres.
This is the Question Number 22, Exercise 17.4 of M.L Aggarwal.

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1. 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

(i)Total surface area of the solid = Base area of the cylinder + Curved surface area of the cylinder + curved surface area of the hemisphere

= r2+2rh + 2r2

= r(r+2h+2r)

= ×600(600+2×1600+2×600)

= 600 ×(600+3200+1200)

= 600 ×(5000)

= 3000000 cm2

= 300 m2

Hence the total surface area of the solid is 300 m2.

(ii)Volume of the solid = Volume of the cylinder + Volume of the hemisphere

= r2h + (2/3) r3

= r2(h+ (2/3)r)

= ×6002(1600+ (2/3)×600)

= 360000 (1600+400)

= 360000 ×2000

= 720000000 cm3

= 720 m3

= 720000 litres [1 m= 1000 litres]

Hence the volume of the solid is 720000 litres.

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