Question

A right circular cone has a radius of x+4 and a height 5 units less than its radius. Express the volume of the cone as a polynomial function. The volume of a cone is V=13πr2h for radius r and height h. Enter π as pi.

Answer 1

• V(x) = (1/3)π(x + 4)²(x - 1) or
• V(x) = (1/3)π(x³ + 7x² + 8x - 16)

Explanation:

Given

• Radius of cone = x + 4 units,
• Height of cone = 5 units less than radius,
• Volume formula.

Solution

We are given the volume formula:

• V = (1/3)πr²h

Find the height:

• h = r - 5
• h = x + 4 - 5 = x - 1

Substitute all into formula:

• V(x) = (1/3)π(x + 4)²(x - 1)

You may keep it as is or simplify:

• V(x) =
• (1/3)π(x² + 8x + 16)(x - 1) =
• (1/3)π(x³ + 8x² + 16x - x² - 8x - 16) =
• (1/3)π(x³ + 7x² + 8x - 16)