Question

twelve cookies are cut from a rectangle of dough measuring 12 inches by 16 inches. How many square inches of dough are left over? Express your answer in terms of pi. I can upload picture

Answer 1

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

$\frac{16}{4}=4\text{ inches}$

now the diameter of one cookie is 4 inches so by this we can find the radius

$\begin{gathered} r=\frac{d}{2} \\ r=\frac{4}{2}=2\text{ inches} \\ \end{gathered}$

now first we find the area of dough which isin rectangle shape

area of rectangle is

$A_1=12*16=192\text{ inches}^2$

now we have to find the area of 12 cookies

area of cookies is

$A_2=12*\pi *r^2=12*\pi *4=48\pi\text{ inches}^2$

now after cut dough for 12 cookies and the left over dough is

Final answer:

$A=A_1-A_2=192-48\pi\text{ inches}^2$