Volume as additive
Recognise volume as additive; find volumes of composite solid figures made of two or more non-overlapping right rectangular prisms
What a learner can do afterwards
- Decompose an L-shaped solid into two cuboids and calculate total volume
- Solve a real-world problem requiring the volume of a composite figure (e.g. a step-shaped structure)
- Explain why splitting a composite solid into rectangular prisms allows calculation of total volume
The lesson
A composite solid is a shape made from two or more boxes joined together, like an L-shape or a staircase. You already know how to find the volume of one rectangular prism: multiply length, width, and height. For a composite solid, split it into separate prisms first.
An L-shaped pool splits into two rectangular sections. Section 1 is 6 m long, 3 m wide, and 2 m deep: that's 6 x 3 x 2 = 36 cubic meters. Section 2 is 4 m long, 2 m wide, and 2 m deep: that's 4 x 2 x 2 = 16 cubic meters. Total volume: 36 + 16 = 52 cubic meters.
Split a composite solid along its natural edges so the pieces don't overlap and don't leave gaps. Then every cubic unit gets counted exactly once.
Split a composite solid into rectangular prisms, find each volume, then add them together for the total.
Watch it
Where it sits
This opens up
Nothing builds on it yet.
Where this leads
8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.