Chapter 8.2, Problem 50P

Suppose you are making a giant chocolate chip cookie for a raffle. You roll out a square slab of cookie dough. Then you use a circular plate that touches the edges of the square slab of cookie dough and cut the cookie out of the dough. What is the area of the extra dough? Write your answer in factored form.

To determine

To find : the area of the extra dough.

Answer to Problem 50P

  $a^2\left(1-\frac{\pi }{4}\right)$

Where a is the length of the side of the square.

Explanation of Solution

Given: A square slab of cookie dough is rolled over and a circular plate that touches the edges of the square slab is used to cut the cookie out of the dough.

Calculation:

Let the length of a side of the square slab of cookie dough is a.

Now, diameter of the circular plate would be a , since the plate is touching the edges of the square slab.

Now area of extra dough is equal to area of plate subtracted from area of square,

  $\begin{array}{l}=a^2-\pi ·{\left(\frac{a}{2}\right)}^2\\ =a^2-\pi ·\frac{a^2}{4}\\ =\frac{4a^2-\pi a^2}{4}\\ =a^2\left(\frac{4-\pi }{4}\right)\\ =a^2\left(1-\frac{\pi }{4}\right)\end{array}$