Need some help with this geometry question please Geometry: Area of Shapes

Question

Suppose that when pizza dough is rolled out it costs 25 cents per square foot, and that sauce and cheese, when spread out on a pizza, have a combined cost of 60 cents per square foot. Let’s say sauce and cheese are always spread out to within 1 inch of the edge of the pizza. Compare the sizes and costs of a circular pizza of diameter 16 inches and a 10-inch-by-20-inch rectangular pizza.

Answer 1

Size and cost Comparison:

The Diameter of the circular pizza is 16 in, the area A of the dough , A(dough) = π (16 )² / 4 = 201.1 in²

The area of Dough of the rectangular 20 x 10 in is A ( dough) = 10in x 20in = 200 in^2

The cost of dough of the circular Pizza = (201.1 in²/144) (ft²/in²) x ( $0.25) = $0.35

The cost of dough of the rectangular Pizza = (200 in²/144)(ft²/in²) x ($0.25) = $0.35

The Diameter of the cheese and sauce is = 16 in - 2(1in) = 14 in , A (ch and Sauce) = π(14)²/ 4 = 153.9 in²

The area of the cheese and sauce in the rectangular pizza = ( 10-2)(20-2)= 8in x 18in = 144 in²

The cost of cheese and sauce in the circular pizza is = (153.9 in²/144)(ft²/in²)( $0.60) = $0.64

The cost of cheese and sauce in the rectangular pizza = (144 in²/144)(ft²/in²)( $0.60) = $0.60

The cost of the 16" circular pizza = $0.35+$0.64 = $0.99

The cost of the 10in x 20in rectangular pizza = $0.35+$0.60=$0.95