pizza diameter

Question

if the toppings on a 24-inch diameter pizza cover a 20-inch diameter circle, what percentage of the pizza's area is not covered in toppings

Answer 1

Hi Meg,

 

The radius of the whole pizza is 12 in.

The radius of the portion of the pizza covered by toppings is 10 in.

 

The area of a circle is πr², where r is the radius.

 

The fraction of the pizza covered by toppings is

 

f_covered = [π(10 in)²] / [π(12 in)²] = 100/144 = 50/72 = 25/36 where the π's and the inches canceled, leaving a pure fraction. 

 

f_covered + fraction_not_covered = 1

 

fraction_not_covered = 1 - fraction_covered = 1 - 25/36 = 36/36 - 25/36 = 11/36 ≈ 0.306

% not covered = f_not_covered X 100% = 30.6%