Find Area Wiped By Wiper Blade

[nycmathguy]

Section 4.1

Question 70

 

[MathLover1]

given:
the length of the wiper mechanism is 25 in
the length of the wiper blade is 14in
hint: you need to subtract the area of (25-14=11)in from the area of 25in because that area is not wiped

A=(1/2)(25^2)*125(pi/180)- (1/2)(11^2)*125(pi/180)
A=681.769239- 131.99052468207117
A=549.78in^2

 

[nycmathguy]

given:
the length of the wiper mechanism is 25 in
the length of the wiper blade is 14in
hint: you need to subtract the area of (25-14=11)in from the area of 25in because that area is not wiped

A=(1/2)(25^2)*125(pi/180)- (1/2)(11^2)*125(pi/180)
A=681.769239- 131.99052468207117
A=549.78in^2

Basically, I need to use the area of a sector formula twice.

Yes?

 

[MathLover1]

yes

 

[nycmathguy]

yes

I suspected that I needed to subtract 14 inches from 25 inches. In any case, I simply would have evaluated using 11 inches for r. It would never, ever cross my mind to use the formula twice, honestly.

In fact, there's nothing in the question, as I see it, that indicates this to be done. Of course, you are right. Practice or not your skills in mathematics is far greater than mine will ever be.

I am hoping that your patience will never run out. Just keep in mind that you are retired (more time to play with math). You taught math for a living. I work 40 full-time overnight hours, which leaves very little time for math.

How about one more for today? This one goes back to September 15.

Find Area of Blue Shaded Region