Question

A right circular cone has a radius of 4x + 5 and a height '2' units less than its radius. Express the volume of the cone as a polynomial function. The volume of a cone is 'V = 1/3 pi r^2 h for radius r and height h.

Answer 1

Answer:
`V=(1)/(3)\pi(64x^3+208x^2+220x+75)`Step-by-step explanation:

The radius of the cone, r = 4x + 5

The height is 2 units less than the radius

h = 4x + 5 - 2

h = 4x + 3

The volume of the cone is given as:

`V=(1)/(3)\pi r^2h`

Substitute r = 4x + 5 and h = 4x + 3 into the formula for the volume

`\begin{gathered} V=(1)/(3)\pi(4x+5)^2(4x+3) \\ V=(1)/(3)\pi(16x^2+40x+25)(4x+3) \\ V=(1)/(3)\pi(64x^3+48x^2+160x^2+120x+100x+75) \\ V=(1)/(3)\pi(64x^3+208x^2+220x+75) \end{gathered}`

The volume of the cone expressed as a polynomial function is:

`V=(1)/(3)\pi(64x^3+208x^2+220x+75)`