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

The volume of a cylinder is given by

Whereas the volume of a cone is given by

Since the cylinder has radius x and height y, its volume is

And since the cone has a radius 2x, its volume is

where h is the height of the cone.

We know that the two volumes are the same, so we can build the equation and solve it for h:

Simplify from both sides:

Divide both sides by 4:

let's solve your equation step-by-step.

4x+2=2x+12

step 1: subtract 2x from both sides.

4x+2−2x=2x+12−2x

2x+2=12

step 2: subtract 2 from both sides.

2x+2−2=12−2

2x=10

step 3: divide both sides by 2.

2x

2

=

10

2

x=5

step-by-step explanation: