Question

a pizza parlor in portland sells a pizza with an 18-inch diameter. a pizza parlor in san anita, peru, sells a pizza with a 30.6-centimeter diameter.
part a: how many square inches of pizza is the pizza from portland? show every step of your work. (1 point)
part b: how many square centimeters of pizza is the pizza from san anita, peru? show every step of your work. (1 point)
part c: if 1 in. = 2.54 cm, which pizza has the larger area? show every step of your work. (1 point)
part d: using the diameter of each pizza, determine the scale factor relationship between the pizzas. (1 point)

Explanation:

Part A

Step1: Find radius of Portland pizza

Radius $r = \frac{\text{diameter}}{2} = \frac{18}{2} = 9$ inches

Step2: Calculate area using circle formula

Area $A = \pi r^2 = \pi \times 9^2 = 81\pi \approx 254.47$ square inches

Part B

Step1: Find radius of San Anita pizza

Radius $r = \frac{\text{diameter}}{2} = \frac{30.6}{2} = 15.3$ centimeters

Step2: Calculate area using circle formula

Area $A = \pi r^2 = \pi \times 15.3^2 = 234.09\pi \approx 735.4$ square centimeters

Part C

Step1: Convert Portland pizza diameter to cm

Diameter $= 18 \times 2.54 = 45.72$ cm

Step2: Find radius in cm

Radius $r = \frac{45.72}{2} = 22.86$ cm

Step3: Calculate Portland area in cm²

Area $A = \pi \times 22.86^2 = 522.5796\pi \approx 1641.8$ cm²

Step4: Compare the two areas

$1641.8 > 735.4$

Part D

Step1: Convert diameters to same unit (cm)

Portland diameter: $18 \times 2.54 = 45.72$ cm; San Anita diameter: 30.6 cm

Step2: Find scale factor (Portland:San Anita)

Scale factor $= \frac{45.72}{30.6} = 1.5$

Answer:

Part A: $\boldsymbol{81\pi \approx 254.47}$ square inches
Part B: $\boldsymbol{234.09\pi \approx 735.4}$ square centimeters
Part C: The Portland pizza has the larger area.
Part D: The scale factor of Portland pizza to San Anita pizza is $\boldsymbol{1.5:1}$ (or $\boldsymbol{\frac{3}{2}:1}$)