Ex.11.3 Q9 Mensuration Solution - NCERT Maths Class 8

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A road roller takes \(750\) complete revolutions to move once over to level a road. Find the area of the road if the diameter of a road roller is \(84\,\rm{cm}\) and length is \(1\,\rm{ m.}\)

 Video Solution
Ex 11.3 | Question 9

Text Solution

What is Known?

Diameter of the road roller and length is given.

What is unknown?

Area of the road.


In one revolution, the roller will cover an area equal to its lateral surface area.


Radius of the road roller

\[\begin{align}r = \frac{{84}}{2}\,\rm{cm} = 42\,\rm{ cm} \end{align}\]

Length of the road roller, \(h = 1\,\rm{m} = 100\, \rm{cm}\)

In \(1\) revolution, area of the road covered

\[ \begin{align} &= 2\pi rh \\&= 2 \times \frac{{22}}{7} \times 42 \times 100\\&= 26400\,{\rm{c}}{{\rm{m}}^2} = 2.64\,{{\rm{m}}^2} \end{align}\]

In \(750\) revolutions area of the road covered

\[\begin{align} &= 750 \times 2.64\,\rm{m^2}\\&= 1980\,\rm{m^2} \end{align}\]

Thus, the area of the road is \(\begin{align}1980\,\rm{m^2}{.} \end{align}\)

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