pizza math problem

Question

The directions on a box of Luigi’s Pizza Mix are as follows: Spread the dough to the edges of a circular pan or a 10-inch by 14-inches rectangular pan.

 If you used the same amount of dough, how large a circular pan would you need to make a pizza of the same area and thickness as one made in the rectangular pan? 

Some of your friends who are coming over for pizza prefer more of the edge crust. Which pizza – the circular one or the rectangular one – is most appropriate for these edge-crust lovers?

Answer 1

Area of the circular pan is (radius^2 x pi). The area of the rectangular pan is 140. So, the circular pan area must equal 140 to be the same:

r^2 x pi = 140

r^2 = 140/pi

r = sqrt(140/pi) = 6.7558

So now we know that the radius of the circular pan must be about 6.75 inches. Now we calculate the circumference of the pan to find its size:

Circumference of a circle is (2 x radius x pi)

= 2 x sqrt(140/pi) x pi (or about 2 x 6.75 x pi)

= 13.35 inches

Area vs crust/circumference:

Both areas are 140, but the circular pan has less circumference. So the rectangular pan will have more crust per area