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.

Answer :

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 :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Surface Area of Right Circular CylinderSurface Area of Right Circular CylinderSurface Area of Right Circular Cylinder52 mins
Surface Area of Right Circular CylinderSurface Area of Right Circular CylinderSurface Area of Right Circular Cylinder49 mins
Surface Area of Cube and CuboidSurface Area of Cube and CuboidSurface Area of Cube and Cuboid49 mins
Surface Area and Volume of SpheresSurface Area and Volume of SpheresSurface Area and Volume of Spheres40 mins
Surface Area and Volume of ConeSurface Area and Volume of ConeSurface Area and Volume of Cone24 mins
10 Important Questions of Surface Area and Volume10 Important Questions of Surface Area and Volume10 Important Questions of Surface Area and Volume51 mins
Quiz | MensurationQuiz | MensurationQuiz | Mensuration42 mins
Surface Area and Volume of Right Circular CylindersSurface Area and Volume of Right Circular CylindersSurface Area and Volume of Right Circular Cylinders42 mins
Surface Area and Volume of Right Circular ConeSurface Area and Volume of Right Circular ConeSurface Area and Volume of Right Circular Cone37 mins
10 Important Questions of Surface Area and Volume10 Important Questions of Surface Area and Volume10 Important Questions of Surface Area and Volume52 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses