SOLUTION: Using the formula v=1/3πr^2H how do I write a simplified algebraic expression for the volume of a cone with a radius of ab^3 and a height of 6b/a?

Question 1209932: Using the formula v=1/3πr^2H how do I write a simplified algebraic expression for the volume of a cone with a radius of ab^3 and a height of 6b/a?
Answer by CPhill(1959) (Show Source): You can put this solution on YOUR website!
Let's break down the problem and substitute the given values into the formula.
Formula:
v = (1/3)πr²H
Given Values:
Radius (r) = ab³
Height (H) = 6b/a
Substitute the Values:
v = (1/3)π(ab³)²(6b/a)
Simplify the Expression:
Square the radius:
(ab³)² = a²b⁶
Substitute the squared radius back into the volume formula:
v = (1/3)π(a²b⁶)(6b/a)
Multiply the terms:
v = (1/3)π * 6 * (a²b⁶ * b / a)
Simplify the numerical terms:
(1/3) * 6 = 2
v = 2π(a²b⁶ * b / a)
Simplify the variables:
a²/a = a
b⁶ * b = b⁷
v = 2πab⁷
Simplified Algebraic Expression:
The simplified algebraic expression for the volume of the cone is:
v = 2πab⁷
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