VOLUME PROBLEMS - BLOCKS

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. Rectangular solids and cubes are blocks.

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 height, given a volume of 3375.

Step 1 | Determine the appropriate formula for the figure in the problem. (Refer to Formula Chart for assistance.) | V = l w h
Step 2 | Substitute values. | V = 3375 l = 45 w = 15 h = height
Step 3 | Solve the equation. | V = l w h 3375 = 45 x 15 x h 3375 = 675 x h 3375 = 675 x h 675 675 5 = h
Step 4 | Write the final answer. | Height is 5