Answer:[tex]V=\frac{1}{3}\pi(64x^3+208x^2+220x+75)[/tex]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:
[tex]V=\frac{1}{3}\pi r^2h[/tex]
Substitute r = 4x + 5 and h = 4x + 3 into the formula for the volume
[tex]\begin{gathered} V=\frac{1}{3}\pi(4x+5)^2(4x+3) \\ V=\frac{1}{3}\pi(16x^2+40x+25)(4x+3) \\ V=\frac{1}{3}\pi(64x^3+48x^2+160x^2+120x+100x+75) \\ V=\frac{1}{3}\pi(64x^3+208x^2+220x+75) \end{gathered}[/tex]
The volume of the cone expressed as a polynomial function is:
[tex]V=\frac{1}{3}\pi(64x^3+208x^2+220x+75)[/tex]
