Question

when sizes of pizzas are quoted in inches, the number quoted is the diameter of the pizza. a restaurant advertises an 8 - inch “personal pizza”. if this 8 - inch pizza is the right size for one person, how many people can be fed by a large 16 - inch pizza?
express your answer numerically.

Explanation:

Step1: Calculate area of 8-inch pizza

The area of a circle is $A = \pi r^2$. For an 8-inch pizza, radius $r = \frac{8}{2} = 4$ inches.
$A_1 = \pi (4)^2 = 16\pi$ square inches.

Step2: Calculate area of 16-inch pizza

For a 16-inch pizza, radius $r = \frac{16}{2} = 8$ inches.
$A_2 = \pi (8)^2 = 64\pi$ square inches.

Step3: Find ratio of the two areas

Divide the area of the large pizza by the small pizza to find how many times larger it is.
$\frac{A_2}{A_1} = \frac{64\pi}{16\pi} = 4$

Answer:

4