Questions: A 6 inch personal pizza has 580 calories, with 240 of those from fat. A 14 inch pizza is cut into 8 slices. Estimate the number of calories in one slice of a 14 inch pizza. Round your answer to the nearest calorie.

A 6 inch personal pizza has 580 calories, with 240 of those from fat. A 14 inch pizza is cut into 8 slices. Estimate the number of calories in one slice of a 14 inch pizza. Round your answer to the nearest calorie.

Solution

Solution Steps

Step 1: Calculate the area of the smaller pizza

Using the formula $A_1 = \pi \left(\frac{D_1}{2}\right)^2$, where $D_1 = 6$ inches, we find $A_1 = \pi \times (6/2)^2 = 28.27$ square inches.

Step 2: Calculate the area of the larger pizza

Similarly, using $A_2 = \pi \left(\frac{D_2}{2}\right)^2$, for $D_2 = 14$ inches, we get $A_2 = \pi \times (14/2)^2 = 153.94$ square inches.

Step 3: Determine the ratio of the areas and solve for C2

Given the total calories in the smaller pizza $C_1 = 580$, the ratio of the areas $\frac{A_2}{A_1} = \frac{C_2}{C_1}$ allows us to solve for $C_2 = C_1 \times \frac{A_2}{A_1} = 3157.78$ calories.

Step 4: Calculate the calories per slice of the larger pizza

Dividing the total calories $C_2 = 3157.78$ by the number of slices $N = 8$ gives us the calories per slice = $\frac{C_2}{N} = 395$ calories.