Question

pizzas are measured by diameter. determine the area of a 6 - inch personal pizza. round your answer to the nearest hundredth. square inches determine the area of a 14 - inch personal pizza. round your answer to the nearest hundredth. square inches a 6 - inch personal pizza has 600 calories. determine the number of calories in the 14 - inch pizza. round your answer to the nearest calorie. there are calories in the 14 - inch pizza. 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. there are calories in one slice of the 14 - inch pizza.

Explanation:

Step1: Find area of 6 - inch pizza

The formula for the area of a circle is $A = \pi r^{2}$, where $r$ is the radius. For a 6 - inch pizza, the diameter $d = 6$ inches, so the radius $r=\frac{d}{2}=\frac{6}{2}=3$ inches. Then $A_1=\pi r^{2}=\pi\times3^{2}=9\pi\approx9\times3.14159 = 28.27$ square inches.

Step2: Find area of 14 - inch pizza

For a 14 - inch pizza, the diameter $d = 14$ inches, so the radius $r=\frac{d}{2}=\frac{14}{2}=7$ inches. Then $A_2=\pi r^{2}=\pi\times7^{2}=49\pi\approx49\times3.14159 = 153.94$ square inches.

Step3: Find calories in 14 - inch pizza

Since the number of calories is proportional to the area of the pizza. Let $C_1 = 600$ calories be the calories in the 6 - inch pizza and $C_2$ be the calories in the 14 - inch pizza. We have the proportion $\frac{C_1}{A_1}=\frac{C_2}{A_2}$. Substituting the values, $\frac{600}{9\pi}=\frac{C_2}{49\pi}$. Cross - multiplying gives $C_2=\frac{600\times49\pi}{9\pi}=\frac{600\times49}{9}\approx3267$ calories.

Step4: Find calories per slice of 14 - inch pizza

A 14 - inch pizza is cut into 8 slices. So the number of calories per slice $C=\frac{C_2}{8}=\frac{3267}{8}\approx408$ calories.

Answer:

28.27
153.94
3267
408