Answer:
Part A) 
Part B) 
Step-by-step explanation:
Part A)
we have the formula of the volume of a cylinder

Solve for h
That means ----> isolate the variable h
Divide both side by πr²

Simplify

Rewrite

Part B) Find the height of a cylinder with a volume of 36π cm3 and a base with a radius of 3 cm
we have


substitute in the formula and solve for h


Answer: (150x3)+((150/2)x5)=(450)+((75)x5)=450+375=825. You would have to pay $825.
The proportion of production that is defective and from plant A is
... 0.35·0.25 = 0.0875
The proportion of production that is defective and from plant B is
... 0.15·0.05 = 0.0075
The proportion of production that is defective and from plant C is
... 0.50·0.15 = 0.075
Thus, the proportion of defective product that is from plant C is
... 0.075/(0.0875 +0.0075 +0.075) = 75/170 = 15/34 ≈ 44.12%
_____
P(C | defective) = P(C&defective)/P(defective)
The premium will cover 14,400 dollars over the course of 5 years.