Question

a pizza shop has the menu shown.
menu
size diameter price
small 8\ $8
medium 10\ $11
large 12\ $15
x - large 14\ $21
which size pizza is least expensive per square inch of pizza?
a. small
b. medium
c. large
d. x - large

Explanation:

Step1: Calculate area of small pizza

The area formula for a circle is $A = \pi r^{2}$, with $r=\frac{d}{2}$. For small pizza, $d = 8$ inches, so $r = 4$ inches. Then $A_{s}=\pi\times4^{2}=16\pi$ square - inches. The cost - per - square - inch $C_{s}=\frac{8}{16\pi}=\frac{1}{2\pi}\approx\frac{1}{2\times3.14}\approx0.16$ dollars per square - inch.

Step2: Calculate area of medium pizza

For medium pizza, $d = 10$ inches, so $r = 5$ inches. Then $A_{m}=\pi\times5^{2}=25\pi$ square - inches. The cost - per - square - inch $C_{m}=\frac{11}{25\pi}\approx\frac{11}{25\times3.14}\approx\frac{11}{78.5}\approx0.14$ dollars per square - inch.

Step3: Calculate area of large pizza

For large pizza, $d = 12$ inches, so $r = 6$ inches. Then $A_{l}=\pi\times6^{2}=36\pi$ square - inches. The cost - per - square - inch $C_{l}=\frac{15}{36\pi}=\frac{5}{12\pi}\approx\frac{5}{12\times3.14}\approx\frac{5}{37.68}\approx0.13$ dollars per square - inch.

Step4: Calculate area of X - large pizza

For X - large pizza, $d = 14$ inches, so $r = 7$ inches. Then $A_{xl}=\pi\times7^{2}=49\pi$ square - inches. The cost - per - square - inch $C_{xl}=\frac{21}{49\pi}=\frac{3}{7\pi}\approx\frac{3}{7\times3.14}\approx\frac{3}{21.98}\approx0.14$ dollars per square - inch.

Since $0.13\lt0.14 = 0.14\lt0.16$, the large pizza is the least expensive per square - inch.

Answer:

C. Large