Question

A car has two wipers which do not overlap. Each wiper has a blade of length 25cm sweeping through an angle of ${115^0}$.Find the total area cleaned at each sweep of the blade?

Answer 1

Hint:
Use the formula for area of sector i.e. $\dfrac{\theta }{{360}} \times \pi {r^2}$, where $\theta $ is the angle made by the sweep and $r$is the length of the blade, find the total area i.e. area of two similar sectors/area cleaned by the blades.

Complete step by step solution:
Given that,
Each wiper has a blade of length 25cm.
Blade sweeping angle is ${115^{\circ}}$
There are 2 sweepers and the area formed by the blades for sweeping is a sector.
So, the area of the sector is $\dfrac{\theta }{{360}} \times \pi {r^2}$.
Where, $\theta $ is the angle made by the sweep and $r$is the length of the blade
There are 2 sweepers, so the total angle made by the blades are,
\[
   \Rightarrow 2 \times \dfrac{\theta }{{360}} \times \pi {r^2} \\
   \Rightarrow 2 \times \dfrac{{115}}{{360}} \times \dfrac{{22}}{7} \times {25^2} \\
   \Rightarrow 1254.96c{m^2}
 \]

So, the total area cleaned at each sweep of the blade is \[1254.96c{m^2}\].

Note:
The area formed by moving one end to another end with an angle is called sector and not segment. Area of segment is the difference between the area of sector and the triangle involved.