Final answer:
The student ate 100.53 square inches of pizza, which is half of the total 201.06 square inches calculated from the pizza's diameter of 16 inches.
Step-by-step explanation:
If the diameter of the pizza is 16 inches, then the radius (r) is half of that, which is 8 inches. To find the area of the pizza, you use the formula for the area of a circle, A = πr^2, where π (pi) is approximately 3.14. Plugging in the numbers, we get:
A = π × (8 inches)^2
A = 3.14 × 64
A = 201.06 square inches (total area)
If you eat half the pizza, you would consume half of the total area:
Half area = 201.06 square inches / 2
Half area = 100.53 square inches
Therefore, you ate 100.53 square inches of pizza.