Question

3. Bouncy rubber balls are composed of a hollow rubber shell 0.4" thick and an outside diameter of 1.2". The price of the rubber needed to produce this toy is $0.035/in3.

a. What is the cost of producing 1 case, which holds 50 such balls? Round to the nearest cent.

b. If each ball is sold for $0.10, how much profit is earned on each ball sold?

Answer 1

a. $ 1.11

b. $ 0.08

Explanation:

a. The volume of the ball is the volume considering all it (1.2 in diameter) less the volume considering the 0.4 in thick.

V = (4/3)πrb³ - (4/3)πrt³

Where rb is the radius of the ball (0.6 in) and rt is the thick (0.4 in)

V = (4/3)π(0.6)³ - (4/3)π(0.4)³

V = 0.637 in³

For 50 balls, the volume is 50*0.637 = 31.85 in³

So, the cost to produce 1 case is:

$0.035/in³ * 31.85 in³ = $ 1.11

b. The profit is the difference between sales and cost, so for one ball:

P = 0.10 - 0.035*0.637

P = $ 0.08