Finding Volumes of Complex Figures
To find the volume of a complex figure, imagine the solid broken up into sections.
Find the volume of each section.
Add the sections together to find the total volume.
Example
Find the volume of the complex figure shown below.
Think
The volume of the triangular prism is already given as 18 cubic feet. The volume of the brown rectangular prism is not known. We need to find the volume of the brown rectangular prism and add it to find the total.
Volume of the rectangular prism
V = l x w x h
V = 6 ft x 3 ft x 3 ft
V = 54 ft 3
Volume of the triangular prism
V = 18 ft 3
Total Volume
54 ft 3 + 18 ft 3 = 72 ft 3
The total volume of the figure is 72 ft 3.
Imagine the complex figure broken into two parts. Find the volume of each, and then add them.
1.
2.
3.
