Acylinder and a cone have the same volume. the cylinder has radius x and height y. the cone has radius 2x. find the height of the cone in terms of y.

The volume of the cone is (x)(x)(y)(pi)

That is equal to the volume of the cone, or 1/3{2x(2x)(height)(pi)}

Set the, equal to each other.

x(x)y(pi)=1/3{2x(2x)(height)(pi)}

Divide pi out from both sides.

x(x)y=1/3{2x(2x)(height)}

Divide X out.

xy=1/3{2(2x)height}

Divide X out again.

y=1/3{4(height)}

Multiply both sides by 3.

3y=4(height)

Since we want the height, isolate it.

3/4y=height

The height of the cone is 3/4y.

Hope this helps!