A car has two wipers which do not overlap. Each wiper has a blade of length 28 cm and sweeps Class 9

A car has two wipers which do not overlap. Each wiper has a blade of length 28 cm and sweeps Class 9

Question 1.

A car has two wipers which do not overlap. Each wiper has a blade of length 28 cm and sweeps through an angle of 120°. Find the total area cleaned at each sweep 4 of the blades. Class 9

Solution:

Angle swept by blade (θ) = 120°

Length of blade = radius of sector (r) = 28 cm

∵ Area swept by one wiper = Area of sector

$\begin{aligned} & =\frac{\theta}{360^{\circ}} \times \pi r^2 \\ & =\frac{120}{360} \times \frac{22}{7} \times(28)^2 \\ & =\frac{1}{3} \times \frac{22}{7} \times 784 \\ & =\frac{1}{3} \times 22 \times 112 \\ & =\frac{2464}{3} \\ & =821.33 \mathrm{~cm}^2\end{aligned}$

∴ Area cleaned by one wiper = 821.33 cm²

∵ There are two wipers and they do not overlap

∴ Total area = 2 × 821.33

= 1642.66 cm²

∴ Toal area cleaned at each sweep = 1642.66 cm²