Question

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

Answer 1

Given,

Radius (r) = 25 cm

Sector angle (θ) = 115°

Since there are two blades,

The total area of the sector made by wiper,

$= 2 \times ( \frac{θ}{360} ) \times \pi {r}^{2}$

$= 2 \times ( \frac{115}{360} ) \times ( \frac{22}{7} ) \times {25}^{2}$

$= 2 \times \frac{158125}{252} \: \: {cm}^{2}$

$= \frac{158125}{126} \: \: {cm}^{2}$

$= 1254.96 \: \: {cm}^{2}$

Answer 2

Given :

• A car has two wipers, Each wiper has a blade of length 25cm.
• A blade of length 25cm sweeping through an angle of 115°.

To find :

• The total area cleaned at each sweep of the blades.

$\;\large\underbrace{\underline{\sf{Understanding\;the\;Concept}}}$

In the question, Given that there are two wipers of a car which don't overlap. The length and angle is given to us. We have to find the total area cleaned at each sweep of the blades.

Solution :

To find the total area cleaned at each sweep of the blades.

Total area cleaned by two wipers = 2 × area cleaned by 1 wiper.

⟹ 2 × area sector with 115°.

⟹ $\sf 2 \times \dfrac {\theta}{360^{\circ}} \times \pi r^2$

⟹ $\sf 2 \times \dfrac {115^{\circ}}{360^{\circ}} \times \dfrac {22}{7} \times 25^2$

⟹ $\sf \dfrac {158125}{126} cm^2$

$\therefore$ Area cleaned by wiper is 1254.96 cm².