Question

johns pizza sells one 16 - inch cheese pizza or two 10 - inch cheese pizzas for $10.99. determine which size gives more pizza. 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 10 - inch pizzas give more pizza with a combined area of □ square inches. b. the 16 - inch pizza gives more pizza with an area of □ square inches.

Explanation:

Step1: Recall the formula for the area of a circle

$A = \pi r^{2}$, where $r$ is the radius of the circle. For a pizza, the diameter is given, and the radius $r=\frac{d}{2}$.

Step2: Calculate the area of a 16 - inch pizza

The diameter $d = 16$ inches, so the radius $r=\frac{16}{2}=8$ inches. Then the area $A_{16}=\pi r^{2}=\pi\times8^{2}=64\pi\approx 64\times 3.14 = 200.96$ square inches.

Step3: Calculate the area of two 10 - inch pizzas

For a 10 - inch pizza, the diameter $d = 10$ inches, and the radius $r=\frac{10}{2}=5$ inches. The area of one 10 - inch pizza is $A_{10}=\pi r^{2}=\pi\times5^{2}=25\pi$ square inches. The area of two 10 - inch pizzas is $A_{2\times10}=2\times25\pi = 50\pi\approx50\times3.14=157$ square inches.

Since $200.96>157$, the 16 - inch pizza has a larger area.

Answer:

B. The 16 - inch pizza gives more pizza with an area of 200.96 square inches.