The volume of a cone varies jointly as the square of its radius and its height. If the volume of a cone is 50π cubic inches when the radius is 5 inches and the height is 6 inches, find the volume of a cone when the radius is 4 inches and the height is 3 inches

Answer 1

50π * (4/5)^2 * (3/6)

Answer 2

So would it be 16

Answer 3

You should know that
volume of cone = (1/3) π r^2 h
if not, then ....

V = k r^2 h
when V = 50π, r = 5, and h = 6
50π = k(25)(6)
k = 50π/(150) = π/3 or (1/3)π , how about that?

V = (1/3)π (4^2)(3) cubic inches = same answer at R_scott,
and certainly not 16

Answer 4

So would it be 16 π ? Ugh lol no matter what I do I keep getting 16. Thank you guys for your help trying to explain to me :)

Answer 5

You are told that
v = k r^2 h
That means that V/(r^2 h) = k, a constant, which does not change. So now you know you are looking for v such that

v/(4^2 * 3) = 50π/(5^2 * 6)
v/48 = 50π/150 = π/3
v = 48π/3 = 16π