Answer:
Step-by-step explanation:
The volume of a cone is
[tex]V=\frac{1}{3}\pi r^2h[/tex]
Filling in what we have:
[tex]104.67=\frac{1}{3}(3.14)r^2(4)[/tex] and simplifying a bit:
[tex]104.67=\frac{1}{3}(12.56)r^2[/tex]
Multiply both sides by 3 to get:
[tex]314.01=12.56r^2[/tex]
Divide both sides by 12.56 to get:
[tex]25.00079618=r^2[/tex] and take the square root of both sides to find the radius:
r = 5
If the radius is 5 and the radius by definition is half the diameter, then the diameter is 10 inches.
