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The total arm and blade of a windshield wiper is 9 in. long and rotates back and forth through an angle of 92 degrees. 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 with the last three decimal places

Question

ellakatherinehavelin ellakatherinehavelin

04-08-2022
Mathematics

contestada

Please Help!
The total arm and blade of a windshield wiper is 9 in. long and rotates back and forth through an angle of 92 degrees. 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 with the last three decimal places

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adioabiola adioabiola · Answer 1 · 2022-08-05T19:05:36+02:00

The area of the region cleaned by the 7-in wiper blade with the angle subtended being 92⁰ as described in the task content is; 39.32in².

What is the area cleaned by the 7-in wiper blade?

According to the task content, it follows that the wiper blade is 7-in long and subtends an angle of 92°.

Consequently, the area swept by the blade in discuss can be determined by the Area of sector formula and hence, is;

Area = (92/360) × (22/7) × 7².

Area = 39.32 in².

Ultimately, it follows from the solving steps above that the area of the region cleaned by the 7-in wiper blade with the angle subtended being, 92⁰ is; Area = 39.32 in².