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3 years ago

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The top and bottom ends of a windshield wiper blade are R = 24 in. and r = 14 in., respectively, from the pivot point. While in

operation, the wiper sweeps through 135°. Find the area swept by the blade. (Round your answer to the nearest whole number.)

1 answer:

Orlov [11]3 years ago

3 0

Answer:

Area swept by the blade = 448 $in^{2}$

Step-by-step explanation:

The arc the wiper wipes is for 135 degrees angle.

So, find area of sector with radius 24 inches. And the find area of arc with r=14 inches.

Then subtract the area of sector with 14 inches from area of sector with radius as 24 inches.

So, area of sector with r=24 in = $\frac{135}{360} *\pi *24^{2}$

Simplify it,

=216 $\pi$

Now, let's find area of sector with radius 14 inches

Area of sector with r=14 in = $\frac{135}{360} *\pi *14^{2}$

Simplify it

=73.5 $\pi$

So, area swept by the blade = 216 $\pi$ -73.5 $\pi$

Simplify it and use pi as 3.14.....

Area of swept =678.584 - 230.907

=447.6769

Round to nearest whole number

So, area swept by the blade = 448 $in^{2}$

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Let's take our answers for $x$ and $y$ and round to 2 decimal places.

$\boxed{x\approx 3.36\ ft}$

$\boxed{y\approx 1.68\ ft}$ </span>

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3 years ago