week 22, problem 2 by: fabian s
DESCRIPTION
Week 22, Problem 2 By: Fabian S. The Problem…. When the diameter of a pizza increases by 2 inches, the area increases by 44%. What was the original the area, in square inches, of the original pizza? Express your answers in terms of pii (3.14). Important things to remember…. - PowerPoint PPT PresentationTRANSCRIPT
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Week 22, Problem 2
By: Fabian S.
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The Problem…
When the diameter of a pizza increases by 2 inches, the area increases by 44%. What was the original the area, in square inches, of the original pizza? Express your answers in terms of pii (3.14)
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Important things to remember…
So the area increases by 44%, And the question asks what was the area, in square inches, of the original Pizza. So the best way to go is to change 44% into a decimal, so then it would be, .44
Remember that the diameter increases 2 inches
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My Explanation
So what I know is that the formula to find the area of the original pizza is, A= Pii (3.14) * r squared. I also squared it because the diameter doubles and the area increases
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My work…To make my life easier I decided to use a circle so I can imagine how it would look
r r+1
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More work…
rr+1
Now I need to find the areas of these 2 circles so for the first circle my area would equal A= pii *r squared and the second circle would be A= Pii * (r+1) squared, A= 1.44(pii * r squared)
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Even more work…
Now I have my two equations that are 1.44( pii* r squared) and 1.44= pii (r squared+ 2r+1). In order to find my answer these two equations need to be equal to each other . So first off I could distribute pii to my equation that is pii (r squared+2r+1) so then it would be…
Pii r squared+2pii r+ Pii
And then it would have to be equal to…
1.44pii r squared
1.44pii r squared= pii r squared+2pii r+ Pii
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More, and more work…
Now I could just simplify more by eliminating my like terms so I could start by eliminating pii r squared…
1.44pii r squared= Pii r squared+ 2pii squared+ pii
So then I will only have…
.44pii r 2= 2 pii r+ pii
Now that I ended up with this I could just divide everything by pii
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The final steps……
So I divide everything by pii…
.44pii r squared= 2pii r+ pii pii pii
So then I will end up getting..
.44r squared= 2r+ pii
Now the final thing to do is check if its equal so my best thing to do is guess and check…
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One last thing…
So when I did my guess and check I tried substituting 5 for r and I was lucky because when I plugged it it both equations equaled 11
.44* 5 squared= 11 2*5+1= 11
So my final answer is 5
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My final answer………
5