Question

The volume of a cone varies jointly as the square of its radius and its height. If the volume of a cone is 2 pi cubic inches when the radius is 1 inch and the height is 6 inches, find the volume of a cone when the radius is 5 inches and the height is 3 inches. Please help!!!!!!! :(

Answer 1

I will assume that we don't know that the volume of a cone
= (1/3)π r^2 h

and let
V = k r^2 h

so just use a ratio:
V/2π = k (25)(3)/ (k (1)(6))
V/2π = 75/6
V = 2π(25/2) = 25π

if we just use our well-known formula:
V = (1/3)π(25)(3) = 25π

or

V = k r^2 h <----- according to your wording.
given: V = 2π when r = 1 and h = 6, so
2π = k(1)(6)
k = 2π/6 = (1/3)π

so V = (1/3)π r^2 h , and there is your formula ! , now just plug in h=5,r=3