/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 70 A car's rear windshield wiper ro... [FREE SOLUTION] | 91影视

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Chapter 4: Problem 70

A car's rear windshield wiper rotates \(125^{\circ} .\) The total length of the wiper mechanism is 25 inches and wipes the windshield over a distance of 14 inches. Find the area covered by the wiper.

Short Answer

Expert verified
The area covered by the wiper is approximately 49.658 square inches.

Step by step solution

01

Compute the radius

Since the total length of the wiper mechanism is given as 25 inches and the wiper wipes a distance of 14 inches (which represents the diameter of the circle), the radius (r) of the circle is half the diameter. So, the radius is given by \(r = \frac{d}{2} = \frac{14}{2} = 7\) inches.
02

Compute the area of the sector

We use the formula for the area of a sector which is: \( Area = \frac{\theta}{360} \times \pi r^{2}\), where \(\theta\) is the central angle. Plugging in the values we have:\( Area = \frac{125}{360} \times \pi \times (7)^2 \).
03

Solve for the area

Carrying out the multiplication, we get that the area is approximately \(49.658\) square inches.

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