Area Calculation for Car Wipers

The problem requires calculating the total area swept by two car wipers that do not overlap.

Sector Area Formula

Each wiper sweeps out a sector of a circle. The area of a sector is calculated using the formula:

\(A_{sector} = \frac{\theta}{360^\circ} \times \pi r^2\)

Where:

• \(r\) is the length of the wiper blade (radius).
• \(\theta\) is the angle swept in degrees.
• \(\pi\) is the constant Pi.

Area Cleaned by One Wiper

Given values:

• Radius, \(r = 18\) cm
• Angle, \(\theta = 126^\circ\)
• \(\pi = \frac{22}{7}\)

Substitute these values into the sector area formula:

\(A_{single} = \frac{126^\circ}{360^\circ} \times \frac{22}{7} \times (18 \text{ cm})^2\)

Simplify the angle fraction:

\(\frac{126}{360} = \frac{7}{20}\)

Calculate the square of the radius:

\((18 \text{ cm})^2 = 324 \text{ cm}^2\)

Calculate the area for one wiper:

\(A_{single} = \frac{7}{20} \times \frac{22}{7} \times 324 \text{ cm}^2\)

Cancel out the 7s:

\(A_{single} = \frac{1}{20} \times 22 \times 324 \text{ cm}^2\)

\(A_{single} = \frac{11}{10} \times 324 \text{ cm}^2\)

\(A_{single} = 1.1 \times 324 \text{ cm}^2 = 356.4 \text{ cm}^2\)

Total Area Calculation

Since there are two wipers and they do not overlap, the total cleaned area is twice the area swept by a single wiper.

\(A_{total} = 2 \times A_{single}\)

\(A_{total} = 2 \times 356.4 \text{ cm}^2\)

\(A_{total} = 712.8 \text{ cm}^2\)

Final Answer

The total area cleaned by the blades is \(712.8 \text{ cm}^2\).