Answer :
Given:
Here twelve cookies are cut from a rectangle of dough measuring 12 inches by 16 inches.
Required:
How many square inches of dough are left over
the radius of cooke is 2 inches because if we cut cookie s in this formation and we get 4 cookies in horizontal so there are 4 diameter of each cookie and the total of these 4 diameter is 16.
So now the measure of one cookie is
[tex]\frac{16}{4}=4\text{ inches}[/tex]now the diameter of one cookie is 4 inches so by this we can find the radius
[tex]\begin{gathered} r=\frac{d}{2} \\ r=\frac{4}{2}=2\text{ inches} \\ \end{gathered}[/tex]now first we find the area of dough which isin rectangle shape
area of rectangle is
[tex]A_1=12*16=192\text{ inches}^2[/tex]now we have to find the area of 12 cookies
area of cookies is
[tex]A_2=12*\pi *r^2=12*\pi *4=48\pi\text{ inches}^2[/tex]now after cut dough for 12 cookies and the left over dough is
Final answer:
[tex]A=A_1-A_2=192-48\pi\text{ inches}^2[/tex]