Question

# A cylindrical roller$2.5m$ in length, $1.75m$ in radius when rolled on a road was found to cover the area of $5500{m}^{2}$. How many revolutions did it make?

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Solution

## Given,Length of a cylindrical roller, $h=2.5m$Radius of a cylindrical roller,$r=1.75m$Total area rolled on a road by a cylindrical roller $=5500{m}^{2}$Hence,Area covered by a cylindrical roller in one revolution = Curved surface area of a cylindrical roller $\begin{array}{rcl}& =& 2\pi rh\\ & =& 2x\frac{22}{7}x1.75x2.5\\ & =& \frac{\left(44x4.375\right)}{7}\\ & =& \frac{\left(192.5\right)}{7}\\ & =& 27.5{m}^{2}\end{array}$Number of revolutions rolled by a cylindrical roller $\begin{array}{rcl}& =& \frac{Totalarearolledbyacylindricalroller}{Arearolledtocoverbyacylindricalrollerinonerevolution}\\ & =& \frac{5500}{27.5}\\ & =& 200\end{array}$Therefore, the number of revolutions rolled by a cylindrical roller on a road is $200$.

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