What fraction of a 6-inch-diameter pizza contains the same amount of pizza as 1 slice of a 12-inch-diameter pizza of the same thickness cut into 12 equal slices?

Step 1: Understand the problem We are comparing two pizzas. One is a 6-inch-diameter pizza and the other is a 12-inch-diameter pizza cut into 12 equal slices. We need to find out what fraction of the smaller pizza is equivalent to one slice of the larger pizza.

Step 2: Calculate the area of the pizzas The area of a circle (which is the shape of our pizzas) is given by the formula πr², where r is the radius of the circle. The radius is half the diameter, so the radius of the 6-inch pizza is 3 inches and the radius of the 12-inch pizza is 6 inches.

Area of 6-inch pizza = π(3)² = 9π square inches Area of 12-inch pizza = π(6)² = 36π square inches

Step 3: Calculate the area of one slice of the 12-inch pizza Since the 12-inch pizza is cut into 12 equal slices, the area of one slice is the total area divided by the number of slices.

Area of one slice = 36π / 12 = 3π square inches

Step 4: Calculate the fraction of the 6-inch pizza that is equivalent to one slice of the 12-inch pizza This is the area of one slice of the 12-inch pizza divided by the total area of the 6-inch pizza.

Fraction = 3π / 9π = 1/3

So, one slice of a 12-inch pizza is equivalent to one third of a 6-inch pizza.