If diameter of a road roller is 0.9m & its length is 1.4 m, how much area of a field will be pressed i its 500 rotations ?
Answers
Height (Length) of the road roller is 1.4m
CSA of the road roller = 2πrh
= 2 × 22/7 × 0.9/2 × 1.4
= 2 × 11/7 × 0.9 × 1.4
= 27.72/7
= 3.96m²
Hence, total area it will cover in 500 rotations = 3.96 × 500
= 1980m²
Hope it's right...
Diameter = 0.9m ; Radius = 0.9/2 = 0.45
Height = 1.4m
We know that, The shape of roller's wheels is like a cylinder.
Therefore, Curved surface area of roller = Curved surface area of roller
Curved surface area of cylinder = 2πrh
= 2 × 22/7 × 0.45 × 1.4
= 44 × 0.2 × 0.45
= 3.96 sq.m
Therefore, Total area pressed by roller in one rotation = 3.96 sq.m
It is given that, The roller rotates 500 times to press the all ground.
∴ Area pressed in 500 rotations = 500 × 3.96
= 1980 sq.m
Therefore, Total area pressed by roller in 500 rotations is 1980sqm.
Explanation:
In the given question, The diameter of road roller is given as 0.9m. First we converted it into radius i.e. 0.45m. The height of the roller was given as 1.4m. Now, As we have to find the outer area/curved surface area of roller. So, we used the formula of Curved surface area of cylinder. By putting the given values in the formula, we find the curved surface area of roller of 1 sqm. It was given that, to find the Area pressed in 500 rotations. So, We multiplied the Curved surface area of roller for 1sqm with 500. And, we get the final answer as 1980 sqm.