Jamie and Joe are eating pizza. Joe eats $\frac{1}{6}$ a 12 inch diameter pizza, while Jamie eats $\frac{1}{4}$ of a 10 inch diameter pizza. Who ate more area of pizza and how much more?
Answer
Final Answer: Jamie ate more pizza. The difference in the area of pizza they ate is approximately \(\boxed{1.767145867644259}\) square inches.
Step 1 ：First, we need to calculate the area of the pizzas that Jamie and Joe ate. The area of a circle is given by the formula \(\pi r^2\), where \(r\) is the radius of the circle.
Step 2 ：Since the diameters of the pizzas are given, we need to divide them by 2 to get the radii. For Joe, the radius is \(\frac{12}{2} = 6.0\) inches. For Jamie, the radius is \(\frac{10}{2} = 5.0\) inches.
Step 3 ：Then, we calculate the areas of the pizzas. For Joe, the area is \(\pi \times 6.0^2 = 18.84955592153876\) square inches. For Jamie, the area is \(\pi \times 5.0^2 = 19.634954084936208\) square inches.
Step 4 ：We multiply the areas of the pizzas by the fractions that Jamie and Joe ate to get the areas of the pizzas that they ate. Joe ate \(\frac{1}{6}\) of his pizza, so he ate \(\frac{1}{6} \times 18.84955592153876 = 3.141592653589793\) square inches of pizza. Jamie ate \(\frac{1}{4}\) of her pizza, so she ate \(\frac{1}{4} \times 19.634954084936208 = 4.908738521234052\) square inches of pizza.
Step 5 ：Finally, we compare the two areas to see who ate more pizza and by how much. Jamie ate more pizza. The difference in the area of pizza they ate is approximately \(4.908738521234052 - 3.141592653589793 = 1.767145867644259\) square inches.
Step 6 ：Final Answer: Jamie ate more pizza. The difference in the area of pizza they ate is approximately \(\boxed{1.767145867644259}\) square inches.
