The exact area of a pizza whose diameter is 12 inches is 36 pi square inches or approximately 113.0973 square inches. The permissible error for the output is five square inches. Thus, the area of a legal pizza must be between 108.0973 square inches and 118.0973 square inches.

Since the area of a pizza of radius R is given by

A = pi R^2

the radius of a pizza whose area is A is given by

Thus, the radius of a legal pizza must be between 5.8659 inches and 6.1312 inches and its diameter must be between 11.7318 inches and 12.2624 inches. Thus, if |diameter - 12| < 0.2624 inches the pizza will be legal.

When the permissible output error is 5 square inches the input tolerance is 0.2624 inches.