Question

1. a large pizza has a diameter of 45 cm. a medium pizza has a diameter of 35 cm. 2 large pizzas costs $24. 3 medium pizzas cost $27.

a) what is the cost of one large pizza?
b) find the cost per cm² for a large pizza.
c) what is the cost of one medium pizza?
d) find the cost per cm² for a medium pizza.
e) which is the better deal?

Explanation:

Step1: Calculate 1 large pizza cost

Divide total cost by quantity: $\frac{24}{2} = 12$

Step2: Find large pizza area

First get radius: $r = \frac{45}{2} = 22.5$ cm. Area formula: $A = \pi r^2 = \pi (22.5)^2 = 506.25\pi \approx 1590.43$ cm²

Step3: Large cost per cm²

Divide 1 pizza cost by area: $\frac{12}{1590.43} \approx 0.0075$

Step4: Calculate 1 medium pizza cost

Divide total cost by quantity: $\frac{27}{3} = 9$

Step5: Find medium pizza area

First get radius: $r = \frac{35}{2} = 17.5$ cm. Area formula: $A = \pi r^2 = \pi (17.5)^2 = 306.25\pi \approx 962.11$ cm²

Step6: Medium cost per cm²

Divide 1 pizza cost by area: $\frac{9}{962.11} \approx 0.0093$

Step7: Compare cost per cm²

Lower value = better deal: $0.0075 < 0.0093$

Answer:

a) $\$12$
b) $\approx \$0.0075$ per cm²
c) $\$9$
d) $\approx \$0.0093$ per cm²
e) The large pizza is the better deal.