VOLUME NOTES
Key Words:
fill
inside (3-D)
capacity
mass
Definition: the amount of space inside a 3-dimensional object
Unit of Measurement/Label: cubic units (in³, ft³, yd³, mm³, cm³, m³)
How to find?
 If the figure is shown as a 3-D grid, count all the cubes. (Hint: shading
layers may be helpful)
Example:
11 cubes in the front layer and 4 of those layers so…
11 + 11 + 11 + 11 (or 11 x 4) = 44 cubic units
OR
(5x4)bottom layer 20 cubes + (3x4)second layer 12
cubes + (2x4)3rd layer 8 cubes + (1x4)top layer 4 cubes
= 44 cubic units
 Rectangular Prism: length x width x height—the length tells how many
cubes are in a row, the width/depth tells how many rows of cubes there
are, and the height tells how many layers there are, which would be
repeated addition.
 Rectangular Prism: area of base x height—since the base is a rectangle
and area of a rectangle is length x width, we are turning a 2-D object into
3-D by including height (# of layers tall), so length x width/depth x height
is the same as area of base (length x width) x height.
Example:
height = 2 in.
width/depth = 4 in.
length = 6 in.
4 rows with 6 cubes in each = 6+6+6+6, which is the same as 6 x 4, equaling 24
cubes, then 2 layers of 4 rows with 6 cubes in each, which is the same as 24+24,
equaling 48 cubes so…
length (6) x width/depth (4) x height (2) = Volume (48 cu. in. or in³)
OR
area of base (24) x height (2) = Volume (48 cu. in. or in³)