# Ex.11.3 Q9 Mensuration Solution - NCERT Maths Class 8

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## Question

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
Mensuration
Ex 11.3 | Question 9

## Text Solution

What is Known?

Diameter of the road roller and length is given.

What is unknown?

Reasoning:

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

Steps:

\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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