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

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Given:

A car has two wipers which do not overlap. Each wiper has a blade of length 25 cm sweeping through an angle of $115^o$.

To do:

We have to find the total area cleaned at each sweep of the blades.

Solution:

The length of the blade of wiper $=$ Radius of sector swept by blade

$= 25\ cm$

Area cleaned by each sweep of the blade $=$ Area of sector swept by the blade

Angle of the sector formed by the blade of the wiper $=115^o$

Area of the sector formed $=\frac{\pi r^{2} \theta}{360^{\circ}}$

$=\frac{22}{7} \times \frac{25 \times 25 \times 115^{\circ}}{360^{\circ}}$

$=\frac{11 \times 25 \times 25 \times 23}{7 \times 36}$

Total area cleaned at each sweep of the blade $=2$ (Area cleaned by one wipe)

$=\frac{2 \times 11 \times 25 \times 25 \times 23}{7 \times 36}$

$=\frac{11 \times 25 \times 25 \times 23}{7 \times 18}$

$=\frac{158125}{126} \mathrm{~cm}^{2}$

The total area cleaned at each sweep of the blades is $\frac{158125}{126} \mathrm{~cm}^{2}$.

Updated on 10-Oct-2022 13:24:02