Composite volume
Let B be the block volume and C the cylinder volume. Add non-overlapping parts or subtract genuinely removed space. Surface contact areas are not volume corrections
- A through-hole The hole length is the distance it travels through the block, not a sloping distance or the block width
- Consistent units Use cubic units for volume. If dimensions use metres and centimetres, convert lengths first
- Join versus overlap Simple addition applies only when the component volumes do not overlap. If there is a real overlapping region, count it once
Worked example
A circular hole of radius 2 cm passes through the 5 cm height of a 12 cm by 8 cm by 5 cm block. Find the remaining volume to 2 decimal places
- \(\displaystyle B=12\times8\times5=480\text{ cm}^3\)Volume of the block before drilling
- \(\displaystyle C=\pi(2)^2(5)=20\pi\text{ cm}^3\)Volume of the removed cylinder
- \(\displaystyle V=(480-20\pi)\text{ cm}^3\)Subtract the removed space before rounding
- \(\displaystyle V\approx417.17\text{ cm}^3\)Final result to 2 decimal places
Common mistakes
Difficulty levels
Questions about this topic
Why is there no contact-face subtraction for volume?+
A contact face is a two-dimensional boundary. When solids only meet at that face, no three-dimensional region is counted twice
Does the hole always have the same height as the block?+
Only for a hole passing vertically through the full block height, as stated in these questions. A horizontal or partial hole has a different length
Can I use outside dimensions to calculate a container’s capacity?+
No. Capacity is usable internal space. These questions describe solid material or a stated removed hole, not an unspecified container interior
Can I use a calculator?+
A calculator is allowed unless a question is marked no calculator
Which year level and chapter is this?+
Year 10 Mathematics, chapter 1: Measurement