VOLUME PROBLEMS - CYLINDERS

Concept: Volume is a measure of the amount of space inside a three-dimensional object. Volume is measured in three dimensional units or cubic units, such as cubic inches, cubic feet, cubic yards, cubic centimeters and other metric units.

Formula Chart
Figure | Name | Formula | Term Meanings
l
h
w
| Rectangular solid | V = l w h | l = length w = width h = height
s
| Cube | V = s 3 | s = side
r
h
| Cylinder |  | r = radius h = height (or length)
| cone |  | r = radius h = height
e (or w ) e
e (or l ) e
| Square pyramid or Rectangular pyramid (Use w and l instead of e 2 for Rectangular pyramids) | or | h = height e = edge or h = height l = length w = width
r w l h
w w l h
| Prism |  | l = length w = width h = height
| Sphere |  | r = radius

Steps for Solving Volume Problems

Step 1 | Determine the appropriate formula for the figure in the problem. (Refer to Formula Chart for assistance.)
Step 2 | Substitute values.
Step 3 | Solve the equation.
Step 4 | Write the final answer.

Example Solve for the diameter, given = 3.14 and volume = 28848.75

Step 1 | Determine the appropriate formula for the figure in the problem. (Refer to Formula Chart for assistance.) |
Step 2 | Substitute values. | V = 28848.75 = 3.14 h = 30 d = diameter (d = 2 x r) r = radius
Step 3 | Solve the equation. | 28848.75 = 3.14 x r 2 x 30 28848.75 = 94.2 x r 2 28848.75 = 94.2 x r 2 94.2 94.2 306.25 = r 2 = r 17.5 = r (Radius x 2 = diameter) 17.5 x 2 = 35
Step 4 | Write the final answer. | Diameter is 35