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° × πr2
= 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 cm2
= 1254.96 cm2
☛ 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 cm2.
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