Answer the question please

Question

The total arm and blade of a windshield wiper is 11 in. long and rotates back and forth through an angle of 94°. The shaded region in the figure is the portion of the windshield cleaned by the 7-in. wiper blade. What is the area of the region cleaned?

Answer 1

A circle of radius 11 inches has an area of

A = πr² = π11² = 121π square inches.

But we're not sweeping out all of this circle. We're missing a smaller circle of radius 11-7 = 4 inches. The area of this smaller circle is A = πr² = π4² = 16π.

So

(area of bigger circle) - (area of smaller circle) = 121π - 16π = 105π square inches.

And we're not even sweeping out all 360 degrees of this area of 105π square inches.

We're sweeping out only 94 of those 360 degrees.

So we're sweeping out only 94/360 of the area of 105π square inches.

So the area we're sweeping out is

(94/360)(105π) square inches.

You can rewrite this as

94·105π/360

and then reduce it to 329π/12 square inches

Answer 2

Draw a diagram.

94° = 94°(π/180°) = 47π/90 = θ

Area = (1/2)r²θ

Area of windshield cleaned =

Area of part of windshield swept by the arm - Area of part of windshield swept by the arm that is not cleaned

= (1/2)(11²)(47π/90) - (1/2)[(11-7)²(47π/90) = (47π/180)(105)