A right circular cone has a radius of 5x+2 and a height 4 units less than its radius

Question

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”.

Quizzma Team · Answer

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 +

1 Answer