Volume of Composite Figures
Concept
A composite solid is a solid that is composed, or made up of, two or more solids. The solids that it is made up of are generally prisms, pyramids, cones, cylinders, and spheres. In order to find the volume of a composite solid, you need to know how to find the volume of prisms, pyramids, cones, cylinders, and spheres.
To calculate the volume of a composite solid, simply split it into smaller solids and calculate their separate volumes. The volumes of each of the individual solids are then added together to give the total volume of the composite solid.
Rules
1. Visualize the composite figure separated into simpler shapes of which you can calculate the volume.
2. Find the volume of each component, then add all of the volumes.
3. State the volumes with the appropriate cubic unit measurements.
Example
Find the volume of the composite figure below.
Solution
Volume of left rectangular prism:
V = l × w × h
V = 5.2 mm × 3 mm × 4 mm = 62.4 mm3
The right, horizontally oriented prism, has dimensions of: 5.8mm, 1.5mm, and 4mm.
Volume of rectangular prism on the right:
V = l × w × h
V = 5.8 mm × 1.5 mm × 4 mm = 34.8 mm3
The total volume: 62.4 mm3 + 34.8 mm3 = 97.2 mm3
Practice Volume of Composite Figures
Practice Problem 1
Find the volume of the figure below. Round your answer to the nearest tenth.
Practice Problem 2
Find the volume of the figure below. Round your answer to the nearest tenth.
Practice Problem 3
The detergent container has dimensions below. Find the volume of this detergent container. Round your answer to the nearest tenth.
Volume: It is the measure of the space occupied by a solid. Volume is measured in cubic units.
Composite solid – a shape composed of a combination of other 3d solids.