Grade 12

Volume of Composite Solids

Lesson

Composite solids are just a combination of simpler solids in disguise.

To find the volume of composite solids such as these:

break down the shape into smaller and simpler solids
find the volume of the individual smaller solids
add up the volumes of the individual solids to find the total volume

The exception to these steps is when the solid we are looking at is more simply considered as a larger solid with a smaller solid cut out of it, like these ones.

In this case we would

identify the large solid as well as the solid that has been cut out of it
find the volume of both pieces
subtract the volume of the cut out piece from the volume of the larger piece

Worked Examples

Question 1

Question 2

Find the volume of the figure shown, correct to two decimal places.

A three-dimensional composite figure which is a combination of a rectangular prism and a half-cylinder. The length of the rectangular prism is labeled as $10$10 m. The base of the rectangular prism has congruent sides as indicated by the single tick mark on each side, with the bottom side labeled $4$4 m. The flat surface of the half cylinder coincides with the top face of the rectangular prism such that its height directly overlaps the rectangle's length. The diameter of the semicircular base of the cylinder is the top side of the base of the rectangular prism.

Outcomes

12CT.D.2.4

Solve problems involving the volumes and surface areas of spheres, right prisms, and cylinders, and of related composite figures, in situations arising from real-world applications