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
1 · Read
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.
2 · Watch
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Where it sits
Where this leads
18 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.