Question

A roller 2 m long has a diameter 140 cm. To level a play ground it takes 350 complete revolutions. Determine the cost of levelling the playground at the rate of

75 paise per square meter.

Answer 1

Diameter of a roller = 140 cm

Radius of the roller :

`=\tt (diameter)/(2)`

`=\tt (140)/(2)`

`= \tt70 \: cm`

Thus, the radius of the roller = 70 cm

Height of roller = 2 m = 2×100 cm = 200 cm

Curved surface area of roller = 1 revolution

The curved surface area of this roller :

`=\tt 2\pi rh`

`= \tt2 * 3.14 * 70 * 200`

`=\tt87920 \: {cm}^(2)`

Thus, the curved surface area of the roller = 87920 cm²

Number of revolutions that needs to be done to level the ground = 350

Distance the roller will travel to get leveled :

`=\tt 87920 * 350`

`= \tt43960000 \: cm`

`= \tt (43960000)/(100) \: m`

`= \tt439600 \: m`

Thus, to level the playground the distance the roller should cover = 539600 m

Cost of covering one square meter of land = 75 Paise

Cost of covering 539600 m of land :

`=\tt 539600 * (75)/(100) \: Rs`

`= \tt (539600 * 75)/(100) \: Rs`

`=\tt (40470000)/(100) \: Rs`

`\color{plum} = \tt\bold{404700 \: rupees}`

Therefore :

▪︎The cost of leveling the playground = 404700 Rs