Question

a pizza shop has the menu shown.
menu

size	diameter	price
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: Recall the area formula for a circle

The area of a circle is given by \( A = \pi r^2 \), where \( r \) is the radius. The radius is half of the diameter, so \( r=\frac{d}{2} \).

Step2: Calculate the area for each pizza size

• Small (d = 8"):

Radius \( r=\frac{8}{2}=4 \) inches.
Area \( A_{small}=\pi(4)^2 = 16\pi \) square inches.

• Medium (d = 10"):

Radius \( r=\frac{10}{2}=5 \) inches.
Area \( A_{medium}=\pi(5)^2 = 25\pi \) square inches.

• Large (d = 12"):

Radius \( r=\frac{12}{2}=6 \) inches.
Area \( A_{large}=\pi(6)^2 = 36\pi \) square inches.

• X - Large (d = 14"):

Radius \( r=\frac{14}{2}=7 \) inches.
Area \( A_{x - large}=\pi(7)^2 = 49\pi \) square inches.

Step3: Calculate the price per square inch for each size

• Small:

Price per square inch \(=\frac{8}{16\pi}=\frac{1}{2\pi}\approx\frac{1}{6.28}\approx0.159\) dollars per square inch.

• Medium:

Price per square inch \(=\frac{11}{25\pi}\approx\frac{11}{78.54}\approx0.140\) dollars per square inch.

• Large:

Price per square inch \(=\frac{15}{36\pi}\approx\frac{15}{113.10}\approx0.133\) dollars per square inch.

• X - Large:

Price per square inch \(=\frac{21}{49\pi}=\frac{3}{7\pi}\approx\frac{3}{21.99}\approx0.136\) dollars per square inch.

Step4: Compare the price per square inch

Comparing the values: \( 0.159\) (Small) \(> 0.140\) (Medium) \(> 0.136\) (X - Large) \(> 0.133\) (Large). So the Large pizza has the least price per square inch.

Answer:

C. Large