VOLUME PROBLEMS - PYRAMIDS

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 width, given a volume of 2,000.

Step 1 | Determine the appropriate formula for the figure in the problem. (Refer to Formula Chart for assistance.) |
Step 2 | Substitute values. | V = 2,000 h = 40 l = 10 w = width 2,000 = x 10 x w x 40
Step 3 | Solve the equation. | 2,000 = x 10 x w x 40 2,000 = 133 x w 2,000 = 133 x w 133 133 15 = w
Step 4 | Write the final answer. | Width is 15