Question

A road roller takes 750 complete revolutions to move once over to level a road. Find the area of the road if the diameter of a road roller is 84 cm and length is 1 m.​

Answer 1

$given \: length \: of \: the \: roller \\ = h \ = 1m \: \\ diameter \: of the \: roller \: = \\ 84 \: cm \\ therefore \: \: radius \: ofthe \: roller \: \\ = r = \frac{84}{2} cm \\ = 42cm \\ = \frac{42}{100} m \\ given \: the \: roller \: takes \: 750 \\ complete \: revolutions \: to \: level \\ \: the \: whole \: road \: . \\ therefore \: area \: of \: the \: road = \\ 750 \times area \: covered \: in1 \: \\ revolution \: . = \\ 750 \times lateral \: surface \: area \\ of \: cylinder. \\ = 750 \times 2\pi \gamma h \\ = 750 \times 2 \times \frac{22}{7} \times \frac{42}{100 } \times 1 \\ = 750 \times 2 \times 22 \times \frac{6}{100} \times 1 \\ = \frac{1500 \times 132}{100} \\ = 15 \times 132 \\ = 1980 {m}^{2}$

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