Width - Pizza Crust

[Guest]

A pizza has a 3" radius for the pizza portion. The pizza has a total area of 25 pi sq. in. due to inclusion of the crust. Determine width of the crust.

Area of a circle - pi * r^2.

3.1416 * 3 * 3 = 28.8744 sq. in.

How do I proceed from this point ?

[Guest]

It is always best to adopt a simple approach....
You are told the total area is 25 x Pi sq.ins
And the inner radius is 3 ins....
We have to find the width of the crust....call it "w"

So then ...Pi x (3 + w)^2 = 25 x Pi
So (3 + w)^2 = 25 x Pi / Pi ....and the Pi cancel

So (3 + w)^2 = 25

So 3 + w = 5

So 4 = 5 - 3 = 2 inches.

...................So Simple............

[Guest]

Sorry....typo error..........
The last line.....So 4 = 5 - 3 = 2 inches.

Should read...So w = 5 - 3 = 2 inches.

.........Simple to make a mistake..........

[Guest]

Thanks.

".........Simple to make a mistake.........." It is.


I have a follow-up question:

A nationally known (probably world as well) pizza chain has a square shaped pizza.

My question - If the total square inches including crust were given, how would the width of that crust be calculated ? I don't have any dimensions.

Thanks again.

[Guest]

Would it not be a good guess to try to do it the same way..........

How did I do the last one?.........

The first thing was to adopt a simple approach.......

You know the Total area...........

Then write an expression for the Total area in terms of the width "w"
And put this equal to the Total area........and solve for "w"

As an example take the same dimension as before.
The pizza bit take as 3 inches square.
The Total area (pizza+crust) is 49 sq. inches
Find "w"

[Guest]

Area of square - S^2

S^2 + 3 = 49

S^2 + 3 - 3 = 49 - 3

S^2 = 46

S^2 / 2 = 46 / 2

S = 23

I am not sure from here.

[Guest]

Your method of solving in beyond any understanding

Compare the question to the first question.

Width = "w". and Total area = 49....so sides are 7 inches long..... (sqroot of 49)
From that you can work out the width is 2 inches by simply (7 - 3)/2 = 2. So w = 2 inches

But using the method of the first question....

(find an expression for the area in terms of "w") = (the Total area given)

(Area of pizza) + (Area of crust) = (the Total Area)

( 3 x 3 ) + ( 2 x ( 7w + 3w )) = 49

So... 9 + 20w = 49

So 20w = 40

So w = 2

.................Simple.................

[Guest]

"(Area of pizza) + (Area of crust) = (the Total Area)

( 3 x 3 ) + ( 2 x ( 7w + 3w )) = 49"

I don't understand this step.

How did you determine the total area would be 49 ?

Thanks.

[Guest]

You were told it was 49 in the question
I gave an example of your query regarding a square pizza

This below is a copy of your query...
"My question - If the total square inches including crust were given, how would the width of that crust be calculated ? I don't have any dimensions."

You were asking "If the total square inches including crust were given" ......."how would the width of that crust be calculated"

All I did was give an example.... I could have picked an area of 36, or 64, or 14, or 16 etc etc

As an example take the same dimension as before.
The pizza bit take as 3 inches square.
The Total area (pizza+crust) is 49 sq. inches
Find "w"

[Guest]

My error - Thanks.