Answer:
20 cm
Step-by-step explanation:
The volume, V, of a cone with radius r and height h is given by the formula
V = [tex](1/3) \pi r^2 h[/tex]
Since it is given that the ratio of h to r is 3/4 we have the relationship
h/r = 3/4 ==> h = (3/4)r
Substituting for h in the volume equation gives us an expression in terms of r
[tex](1/3)\pir^2h = (1/3) \pi r^2 (3/4)r\\(1/3 ) (3/4) = 1/4\\[/tex]
So the expression simplifies to[tex](1/4)\pi r^3[/tex]
We are given that this volume is 2000π cm³
So
(1/4)πr³ = 2000π
Eliminating π on both sides and multiplying by 4 on both sides gives
r³ = 8000
r = ∛8000 = 20 cm Answer
