Question

A 12 inch-diameter pizza and a 16 inch-diameter pizza are each cut into eight congruent slices. Jane ate three slices of the 12 inch pizza. Mark ate three slices of the 16 inch pizza. How many more square inches of pizza did Mark eat than Jane? Express your answer as a common fraction in terms of pi.

Answer 1

They both ate 3/8 of a pizza. Therefore, the quantity that Mark ate in excess of Jane is simply 3/8 × the difference in total area of the pizzas. The 16'' pizza has 64π area, and the 12'' pizza has 36π area, making for a difference of 28π. 3/8 × 28π = 21/2π = 10.5π

Answer 2

Area of 16inch pizza = (pi) r^2 = 64pi
Area of 12 inch pizza = (pi) r^2 = 36pi
Jane ate 3 slices of 12" pizza = 3/8 × 36 = 13.5pi
Mark ate 3 slices of 16" pizza = 3/8×64 = 24pi
Difference Mark ate than Jane = 24-13.5 = 10.5pi (sq inches)