Question

10. A cylindrical roller rolls over 400 times
to completely cover a sports ground. If
the length of the roller is 3.5m and its
radius is 1.4m, find the area of the field.
doubled​

Answer 1

Question:-

A cylindrical roller rolls over 400 times

to completely cover a sports ground. If

the length of the roller is 3.5m and its

radius is 1.4m, find the area of the field.

Formulas used:-

CSA of a cylinder = 2πrh, where r is radius and h is height

Given:-

r = radius = 1.4 m

l = h = height = length = 3.5 m

Number of revolutions = 400

Answer:-

Since only the curved part of the cylinder rolls over a surface, we will be dealing with the CSA (Curved Surface Area).

Area covered when the roller rolls once = CSA of cylinder

Finding CSA of cylinder:-

CSA = 2πrh

=> 2 * 22/7 * 1.4 * 3.5 m²

=> 2 * 22/7 * 14/10 * 35/10 m²

=> 30.8 m²

Area covered in one roll = 30.8 m²

Area covered in 400 rolls = 30.8 * 400 m² = 12,320m² = Area of field

Answer = 12,320 m²