55. You have an empty cone and a cylinder filled with water. The cone has a diameter of 8 and a height of 9. The cylinder has a diameter of 10 and a height of 12. If you dump the water from the cylinder into the cone until it is filled, what volume of water will remain in the cylinder

  252π ≈ 791.7 cubic units

Step-by-step explanation:

The relevant volume formulas are:

  cone: V = 1/3πr²h

  cylinder: V = πr²h

  the radius is half the diameter

__

The volume of the cone is ...

  V = 1/3π(4²)(9) = 48π . . . cubic units

The volume of the cylinder is ...

  V = π(5²)(12) = 300π . . . cubic units

The volume of water remaining in the cylinder after the cone is filled is ...

  cylinder volume - cone volume

  = 300π -48π = 252π ≈ 791.7 . . . cubic units

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: