Question

A cylinder 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.

Please I need help and fast.

Answer 1

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