Question

A toy piece made from plastic is in the shape of a solid hemisphere with a radius of 1.5 centimeters.







There are two types of plastic that can be used to make the hemisphere. Plastic A contains 1.3 grams per cubic centimeter and costs $0.09 per gram. Plastic B contains 1.0 gram per cubic centimeter and costs $0.12 per gram.

Question 1
,begin emphasis,Part A,end emphasis,
Which plastic would result in the lower cost to make the piece? Use 3.14 as an approximation for pi.

Question 1 Answer options with 2 options
A.
Plastic A

B.
Plastic B

Question 2
,begin emphasis,Part B,end emphasis,
What is the cost, to the nearest cent, to make one piece using the cheaper plastic? Enter the answer in the box.

Question 2 Response area with 1 text input box
$

Answer 1

Volume of hemisphere = (2/3)πr^3 = (2/3)π(1.5)^3 = 2.25π ≈ 2.25(3.14) = 7.065 cm^3.

Plastic A: mass = 1.3·7.065 = 9.1845 g; cost = 9.1845·$0.09 = $0.826605 ≈ $0.83.
Plastic B: mass = 1.0·7.065 = 7.065 g; cost = 7.065·$0.12 = $0.8478 ≈ $0.85.

Part A: Plastic A (cheaper).
Part B: $0.83.