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Question

The diameter of a roller 120 cm long is 84 cm. If it takes 500 completed revolutions to level a play ground, determine the cost of levelling it at the rate of Rs. 2.50 per square metre.

Solution
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Roller is in the form of a cylinder as shown in the image.
Given, h=120 cm,
Radius r=Diameter2=842=42 cm
Area covered by the roller in one revolution = Curved Surface Area of the cylinder =2πrh
=2×227×42×120
=31,680 cm2
Area covered in 500 revolutions =(31,680×500) cm2=15,84,000 cm2
Area of playground in m2=15840000100×100 m2=1584 m2
Cost of levelling the playground per m2= Rs. 2.50
Cost of levelling the playground=1584×2.50= Rs. 3960

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