Q. 94.8( 14 Votes )
The length of a road roller is 2.1m and its diameter is 1.4m. For levelling ground 500 rotations of the road roller were required. How much area of ground was leveled by the road roller? Find the cost of levelling at the rate of Rs. 7 per sq. m.
The road roller is cylindrical in shape as described.
Given: length of cylindrical road roller (h) = 2.1 m
Diameter of the road roller = 1.4 m
⇒ Radius of the cylindrical road roller (r) = 1.4 /2 = 0.7 m
The figure is given below:
When the cylindrical road roller will roll on the ground, the only portion of the cylinder that will touch the ground is the curved surface of cylindrical road roller.
Thus, if we find curved surface area of cylinder, we can know area of ground levelled.
Curved surface area of cylinder is given by,
CSA = 2πrh
Where h = height of cylinder when placed vertical or length of the cylinder when placed horizontal
Substituting values in above equation, we get
⇒ CSA = 9.24
This implies that, area of ground leveled in 1 rotation = 9.24 m2
Then, area of ground leveled in 500 rotations = 9.24 × 500 = 4620 m2
If cost of levelling 7 m2 ground = Rs. 7
Then cost of levelling 4620 m2 ground = 4620 × 7 = Rs. 32340
Thus, area of the ground that was levelled by the road roller is 4620 m2 and cost of levelling it is Rs. 32340.
Rate this question :
If diameter of a road roller is 0.9 m and its length is 1.4 m, how much area of a field will be pressed in its 500 rotations?MHB - Math Part-II
The inner diameter of a well is 4.20 metre and its depth is 10 metre. Find the inner surface area of the well. Find the cost of plastering it from inside at the rate Rs.52 per sq.m.MHB - Math Part-II
The length of a road roller is 2.1m and its diameter is 1.4m. For levelling ground 500 rotations of the road roller were required. How much area of ground was leveled by the road roller? Find the cost of levelling at the rate of Rs. 7 per sq. m.MHB - Math Part-II
Curved surface area of a cylinder is 1980 cm2 and radius of its base is 15cm. Find the height of the cylinder.
(π = 22/7)MHB - Math Part-II