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# 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

**Solution:**

Let's draw a figure according to the given question.

Visually it is clear that the area cleaned at the sweep of blades of each wiper = Area of the sector with angle 115° at the center and radius of the circle 25 cm.

There are 2 wipers of the same blade length and same angle of sweeping. Also, there is no area of overlap for the wipers.

∴ Total area cleaned at each sweep of the blades = 2 × Area cleaned at the sweep of each wiper.

Area cleaned at the sweep of each wiper = Area of the sector of a circle with radius 25 cm at an angle of 115°

= θ/360° × πr^{2}

= 115°/360° × π × 25 × 25

= 23/72 × 625π

There are two identical blade-length wipers.

∴ Total area cleaned at each sweep of the blades = 2 × 23/72 × 625π

= 2 × 23/72 × 22/7 × 625

= (23 × 11 × 625)/(18 × 7)

= 158125/126 cm^{2}

= 1254.96 cm^{2}

**☛ Check: **NCERT Solutions for Class 10 Maths Chapter 12

**Video Solution:**

## 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.

NCERT Solutions Class 10 Maths Chapter 12 Exercise 12.2 Question 11

**Summary:**

The total area cleaned at each sweep of the blades of a car having two non-overlapping wipers of blade length 25 cm each sweeping through an angle of 115° is 1254.96 cm^{2}.

**☛ Related Questions:**

- Find the area of a sector of a circle with radius 6 cm if angle of the sector is 60°.
- Find the area of a quadrant of a circle whose circumference is 22 cm.
- The length of the minute hand of a clock is 14 cm. Find the area swept by the minute hand in 5 minutes.
- A chord of a circle of radius 10 cm subtends a right angle at the centre. Find the area of the corresponding : (i) minor segment (ii) major sector. (Use π = 3.14)

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