D. Volume of Composite Objects

Much like finding the area of composite figures using basic shapes, and finding the surface area of composite objects using basic objects, begin to find the volume of a composite object by identifying the basic objects that make up that composite object. Next, determine the volume of each individual object, attending to any necessary missing dimensions or alterations to their formulas. Then, add or subtract some of these volumes to determine the volume of the given composite object.

Example 1

Recall the Lido Beach cabana examples from earlier in the lesson, where each roof had a diameter of 2 metres, each wall had a height of 1.85 metres, and each roof had a slant height of 1.35 metres. What is the volume of one cabana, to the nearest hundredth of a cubic metre?

There is no measurement given for the height of the cone, so use the Pythagorean theorem to determine the height.

The hypotenuse of the right triangle is 1.35 m and the length of the other leg is half of 2 m because the cone is a right cone and thus the centre of the base is located directly below the apex.

The volume can now be determined.

The volume of one cabana is approximately 6.76 m3.

For an example about finding the volume of a composite object see p. 84 of Mathematics 10.