Question

Road roller 140 cm long and 77 cm in diameter makes 100 revolutions to level a field completely. Find the area in (sq.m) of the field. *

Answer 1

Given data : Road roller 140 cm long and 77 cm in diameter makes 100 revolutions to level a field completely.

To find : The area in (sq.m) of the field ?

Solution : We need to find, first in one revolution how much area will road roller covered.

Now, by given ::

Let, height of road roller be 140 cm.

⟹ Height of road roller, h

= 140 cm = 1.4 m

and

⟹ Diameter of road roller, d

= 77 cm = 0.77 m

⟹ Radius of road roller, r

= d/2 = 0.77/2

⟹ Radius of road roller, r

= 0.385 m

Now, to find curved surface area of road roller we use formula,

⟹ curved surface area of cylinder

= 2 * π * r * h

⟹ curved surface area of cylinder

= 2 * 22/7 * 0.385 * 1.4

⟹ curved surface area of cylinder

= 2 * 22 * 0.385 * 0.2

⟹ curved surface area of cylinder

= 44 * 0.385 * 0.2

⟹ curved surface area of cylinder

= 16.94 * 0.2

⟹ curved surface area of cylinder

= 3.388 m²

Hence, area covered by road roller in one revolution is 3.388 m².

Now, to find area covered by road roller in 100 revolution ::

⟹ area covered by road roller

= 3.388 * 100

⟹ area covered by road roller

= 338.8 m²

Answer : Hence, the area of the field is 338.8 m².

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