The area as a function of b is given by
You want to find b such that a(b) = 36.
... (2/3)b^3 +6b = 36
... b^3 +9b -54 = 0 . . . . multiply by 3/2 to clear fractions
A graphing calculator shows this equation to have one real solution at b=3.
The value of b is 3.
Let us assume total capacity of the container = x pounds.
Container contains 1/6th coffee of total x pounds, that is x/6 pounds.
We also given that 1/6th part is equal to 2/3 of a pound.
So, we could setup an equation now.
x/6 pounds equals 2/3 of a pound.
Dividing both sides by 1/6, we get
÷
=
÷
.
Therefore, x = ÷
Division expression that represents the capacity of the container = 2/3 ÷ 1/6.