A cylindrical roller $2.5 m$ in length, $1.75 m$ 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, $h = 2.5 m$
Radius of a cylindrical roller, $r = 1.75 m$
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
$\begin{array}{rcl} = & 2 π r h \\ = & 2 x \frac{22}{7} x 1.75 x 2.5 \\ = & \frac{(44 x 4.375)}{7} \\ = & \frac{(192.5)}{7} \\ = & 27.5 m^{2} \end{array}$
Number of revolutions rolled by a cylindrical roller
$\begin{array}{rcl} = & \frac{T o t a l a r e a r o l l e d b y a c y l i n d r i c a l r o l l e r}{A r e a r o l l e d t o c o v e r b y a c y l i n d r i c a l r o l l e r i n o n e r e v o l u t i o n} \\ = & \frac{5500}{27.5} \\ = & 200 \end{array}$
Therefore, the number of revolutions rolled by a cylindrical roller on a road is $200$ .

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A cylindrical roller2.5m in length, 1.75m in radius when rolled on a road was found to cover the area of 5500m2. How many revolutions did it make?

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