A right circular cone has a radius of 5x+2 and a height 4 units less than its radius. Express the volume of the cone as a polynomial function.
The volume of a cone is given by V= 31
πr 2 h for radius r and height h.
Enter π as “pi”.
A right circular cone has a radius of 5x+2 and a height 4 units less than its radius
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To find the volume of the cone, we’ll use the formula for the volume of a cone:
[
V = frac{1}{3} pi r^2 h
]
where (r) is the radius and (h) is the height.
1. Identify the radius and height:
– The radius (r) is given as (5x + 2).
– The height (h) is 4 units less than the radius, which means:
[
h = r – 4 = (5x + 2) – 4 = 5x – 2
]
2. Substitute (r) and (h) into the volume formula:
[
V = frac{1}{3} pi (5x + 2)^2 (5x – 2)
]
3. Calculate ((5x + 2)^2):
[
(5x + 2)^2 = 25x^2 + 20x + 4
]
4. Multiply ( (25x^2 + 20x + 4) ) by ( (5x – 2) ):
[
begin{align*}
V &= frac{1}{3} pi (25x^2 + 20x +