• Support PF! Buy your school textbooks, materials and every day products via PF Here!

Help with Area of a Sector

1. Homework Statement
The total arm and blade of a single windshield wiper was 10 in. long and rotated back and forth through an angle of 95°. A portion of the windshield is cleaned by 7-in. wiper blade. What is the area of the region cleaned?


2. Homework Equations
Area of a sector = 1/2 r2θ


3. The Attempt at a Solution
My first guess was to simply calculate the area cleaned by the blade and I thought that would be my answer.

In the book though, they calculated the area not cleaned by the blade (r would be equal to (10-7)2) and subtracted it from the total area. I can't wrap my head around that. Why subtract the two areas? Why not just calculate the area that was cleaned by the blade? My guess is it has something to do with the actual angle or radius, but I'd like a little clarification to make sure I really understand this. Thanks!
 

Attachments

tiny-tim

Science Advisor
Homework Helper
25,790
247
hi theintarnets! :smile:

there is a difference between θ/2 * (102 - 72) and θ/2 * (10 - 7)2

which one is correct?
 
They were using the portion not cleaned by the blade which was equal to 3 in., so (10-7) was used for r, and then squared.
 
Last edited:

tiny-tim

Science Advisor
Homework Helper
25,790
247
so they used θ/2 * (102 - 32) ?

what do you think is wrong with that?

what do you think it should be?
 
473
13
3. The Attempt at a Solution
My first guess was to simply calculate the area cleaned by the blade and I thought that would be my answer.
OK, well, that's what the question asks for. Show us how you would do that.

Imagine a worn-out wiper arm, total length 10", that only has 1" of cleaning blade at the end. How would that calculation look different?
 
What I had done was just use 7 for r, thinking that since the cleaning blade was 7 inches, the area cleaned would be 1/2*(7)^2*whatever 95 degrees in radians is. But they way you put it does make me think about it a little more. I guess the area cleaned by blade 1 inch long is much more different than the area cleaned by the last inch of a 10 inch blade. So then the only way to figure it out would be to get the whole area, then subtract the area that the blade isn't cleaning. Am I right?
 

tiny-tim

Science Advisor
Homework Helper
25,790
247
yup! :biggrin:
 

HallsofIvy

Science Advisor
Homework Helper
41,698
871
Did you draw a picture? One thing you need to know, that you did not state, is that the 7" 'cleaning' part of the wiper is at the end of the 10" wiper. IF the 'cleaning' part had started at the pivot point, then you would only need the 7" part. Of course, anyone who has looked at a windshield wiper knows the 'cleaning' part is at the end opposite the wiper.
 

Related Threads for: Help with Area of a Sector

  • Posted
Replies
5
Views
5K
  • Posted
Replies
1
Views
668
  • Posted
Replies
7
Views
727
  • Posted
Replies
7
Views
975
  • Posted
Replies
5
Views
6K
  • Posted
Replies
1
Views
1K

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving

Hot Threads

Top