Question

A car has two wipers which do not overlap. Each wiper has a blade of length 25 cm sweeping through an angle of ${120}^{\circ }$. Find the total area cleaned at each sweep of the blades. (use $\pi$ = $\frac{22}{7}$)

• A. 1750.5 ${cm}^2$
• B. 1600 ${cm}^2$
• C. 1450.9 ${cm}^2$
• D. 1309.5 ${cm}^2$

Answer 1

The correct option is D 1309.5 ${cm}^2$

Area swept by each wiper = Area of sector = $\frac{x^{\circ }}{{360}^{\circ }}$$\times$$\frac{22}{7}$$\times$ $r^2$

Since the angle subtended by the sector at the centre = ${120}^{\circ }$ and radius = 25 cm

So, Area swept by each wiper
= $\frac{{120}^{\circ }}{{360}^{\circ }}$$\times$$\frac{22}{7}$$\times$ ${25}^2$
= 654.76 ${cm}^2$

As, the area cleaned by each sweep of the blade of each wiper is equal

So, total area cleaned at each sweep of the blades = 2 $\times$ 654.76 = 1309.52 ${cm}^2$