NCERT Class X Chapter 11: Area Related To Circles Exercise 11.1 Question 11

NCERT Class X Chapter 11: Area Related To Circles

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.

Given:

Length of each wiper blade, \( r = 25 \) cm
Angle swept by each wiper, \( \theta = 115^\circ \)

To Find:

Total area cleaned at each sweep of the blades.

Formula:

Area of a sector of a circle:
$$ \text{Area} = \frac{\theta}{360^\circ} \times \pi r^2 $$ where \( \theta \) is in degrees.

Solution:

Step 1: Find the area cleaned by one wiper using the sector formula.

$$ \text{Area by one wiper} = \frac{115^\circ}{360^\circ} \times \pi \times (25)^2 $$

Step 2: Substitute the values and simplify.

$$ = \frac{115}{360} \times \pi \times 625 $$

Step 3: Calculate the numerical value.

$$ = 0.3194 \times 3.1416 \times 625 $$

Step 4: Multiply to get the area cleaned by one wiper.

$$ = 0.3194 \times 1963.495 $$ $$ \approx 626.1\ \text{cm}^2 $$

Step 5: Find the total area cleaned by both wipers (since there is no overlap).

$$ \text{Total area cleaned} = 2 \times 626.1 = 1252.2\ \text{cm}^2 $$

Result:

The total area cleaned at each sweep is approximately \( 1252.2\ \text{cm}^2 \).

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