Question

analyze this situation and determine how much cookie dough is "wasted" when 3-inch cookies are cut. then have each team member calculate the amount of dough wasted when a cookie of a different diameter is used. compare results

Answer 1

The result is the same.

Explanation:

I think your question is missed of key information, allow me to add in and hope it will fit the original one.

Please have a look at the attached photo.

My answer:

Given the information:

• square 12 inches wide
• 3-inch diameter cookies are cut => its radius is: 1.5 inches

Hence we can find some information:

• The area of the square is:
  `12^(2) = 144` square inches
• The area of a cookies is:
  `r^(2)`π = 3.14*
  `1.5^(2)` = 7.065 square inches
• The total number of 3-inch cookies are: 4*4 =16

=> The total area of the cookies is: 16* 7.065 = 113.04 square inches

=> how much cookie dough is "wasted" when 3-inch cookies are cut:

= The area of the square - The total area of the cookies

= 144 - 113.04 = 30.96 square inches

If the diameter is increased to 4 inches => its radius: 2 inches, we have:

• The area of a cookies is:
  `r^(2)`π =
  `2^(2) *3.14 = 12.56` square inches
• The total number of 3-inch cookies are: 3*3 =9

=> The total area of the cookies is: 9* 12.56 = 113.04 square inches

=> how much cookie dough is "wasted" when 4-inch cookies are cut:

= The area of the square - The total area of the cookies

= 144 - 113.04 = 30.96 square inches

The result is the same.