Question

patsys pizza sells one 20 - inch cheese pizza or two 12 - inch cheese pizzas for $11.99. determine which size gives more pizza. (a = πr²) select the correct choice below and fill in the corresponding answer box to complete your choice. (round to two decimal places as needed.) a. the 12 - inch pizzas give more pizza with a combined area of □ square inches. b. the 20 - inch pizza gives more pizza with an area of □ square inches.

Explanation:

Step1: Calculate area of 20 - inch pizza

The radius $r_1$ of a 20 - inch pizza (diameter $d_1 = 20$ inches) is $r_1=\frac{d_1}{2}=\frac{20}{2}=10$ inches. Using the formula $A = \pi r^{2}$, the area $A_1=\pi\times(10)^{2}=100\pi\approx 100\times 3.14159 = 314.16$ square inches.

Step2: Calculate area of one 12 - inch pizza

The radius $r_2$ of a 12 - inch pizza (diameter $d_2 = 12$ inches) is $r_2=\frac{d_2}{2}=\frac{12}{2} = 6$ inches. Using the formula $A=\pi r^{2}$, the area of one 12 - inch pizza is $A_{21}=\pi\times(6)^{2}=36\pi$ square inches.

Step3: Calculate area of two 12 - inch pizzas

The combined area of two 12 - inch pizzas $A_2 = 2\times A_{21}=2\times36\pi = 72\pi\approx72\times3.14159=226.19$ square inches.

Step4: Compare the areas

Since $314.16>226.19$, the 20 - inch pizza has a larger area.

Answer:

B. The 20 - inch pizza gives more pizza with an area of 314.16 square inches.