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.

# 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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Given height of the cylinder, h = 8 cmRadius of the cylinder, r = 3 cmRadius of hemisphere , r = 3 cmScale = 1:200Hence actual radius, r = 200×3 = 600Actual 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= r^{2}+2rh + 2r^{2}= r(r+2h+2r)= ×600(600+2×1600+2×600)= 600 ×(600+3200+1200)= 600 ×(5000)= 3000000 cm^{2}= 300 m^{2}Hence the total surface area of the solid is 300 m^{2}.(ii)Volume of the solid = Volume of the cylinder + Volume of the hemisphere= r^{2}h + (2/3) r^{3}= r^{2}(h+ (2/3)r)= ×600^{2}(1600+ (2/3)×600)= 360000 (1600+400)= 360000 ×2000= 720000000 cm^{3}= 720 m^{3}= 720000 litres [1 m^{3 }= 1000 litres]Hence the volume of the solid is 720000 litres.