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…

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

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

My work…To make my life easier I decided to use a circle so I can imagine how it would look

r r+1

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)

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

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

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…

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

My final answer………

5