Question

Question 11
A car has two wipers which do not overlap. Each wiper has a blade of length 25 cm sweeping through an angle of ${115}^{\circ }$. Find the total area cleaned at each sweep of the blades.

Answer 1

Angle of the sector of circle made by wiper $={115}^{\circ }$
Radius of wiper = 25 cm
Area of the sector making angle $\theta$
$=\left(\frac{\theta }{{360}^{\circ }}\right)\times \pi r^2$
Area of the sector made by wiper
$=\left(\frac{{115}^{\circ }}{{360}^{\circ }}\right)\times \pi r^{2}c{m}^2$
$=\frac{23}{72}\times \frac{22}{7}\times {25}^2$
$=\frac{23}{72}\times \frac{22}{7}\times 625c{m}^2$
$=\frac{158125}{252}c{m}^2$
Total area cleaned at each sweep of the blades
$=2\times \frac{158125}{252}c{m}^2$
$=\frac{158125}{126}=1254.96c{m}^2$