Question

A cylindrical roller 2.5 in length, in radius 1.5 when rolled on the road was found to cover the area 16500m2. How many revolutions does it make? Hence find the volume of the roller.

Answer 1

Analysis

In this question, we have to:

→ Find the CSA [Area covered in one revolution]

→ Find the total no. of revolutions to level the specific area.

→ Volume of the roller

Solution:

Length [Height] = 2.5 m

Radius = 1.5 m

Area covered in one revolution = CSA of the cylinder

CSA = 2πrh

= $2\times\dfrac{22}{7}\times1.5\times2.5$

=$\dfrac{165}{7}$

Area of total levelled road = 16500 m²

No. of revolutions required: $\dfrac{Area\:of\:levelled\:road}{CSA}$

= $16500\times\dfrac{7}{165}$

= 700 revolutions

Volume of a cylinder = πr²h

= $\dfrac{22}{7}\times1.5\times1.5\times2.5$

= 17.67 cm³

Therefore,

700 revolutions are required.

           and

Volume of cylinder is 17.67 cm³.