Acylinder and a cone have the same volume. the cylinder has radius x and height y. the cone has radius 3x. find the height of the cone in terms of y.

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Volume of cylinder = pi * radius^2 * height
volume of cone = (1/3) * pi * radius^2 * height

now, we know that the two volumes are equal:
pi * rcyl^2 * hcyl = (1/3) * pi * rcon^2 * hcon
the pi will cross out from both sides.
Now, we substitute:
x^2 * y = (1/3) * (3x)^2 * hcon
x^2 * y = (1/3) * 9x^2 * hcon
the x^2 will cross out from both sides and (1/3)(9)=3
y = 3hcon
hcon = y/3