Volume by displacement (irregular solids)
Theory
Lower an irregular solid into water and read how far the level rises. The rise equals the volume: after \(-\) before. A rise of \(80\) mL means \(80\,\text{cm}^3\).
Displacement is a way to measure the volume of an irregular solid by lowering it into water and reading how far the level rises.
A solid that sinks pushes aside its own volume of water. That water has nowhere to go but up, so the rise in the level equals the volume of the object.
Read the level before and after, then subtract. Because \(1\) mL of water fills exactly \(1\,\text{cm}^3\), a rise in millilitres is the same number of cubic centimetres.
Look at how far apart the marks are before reading a level.
| Before | After | Rise | Volume |
|---|---|---|---|
| \(300\) mL | \(380\) mL | \(80\) mL | \(80\,\text{cm}^3\) |
| \(250\) mL | \(265\) mL | \(15\) mL | \(15\,\text{cm}^3\) |
| \(100\) mL | \(145\) mL | \(45\) mL | \(45\,\text{cm}^3\) |
The volume number is the same as the rise, only the unit changes from mL to \(\text{cm}^3\).
Measuring volume by displacement
- Read the water level before the object goes in.
- Lower the object in so it sinks fully under the water.
- Read the new, higher level.
- Subtract the before reading from the after reading. That rise is the volume, in \(\text{cm}^3\).
| \(V\) | \(=\) | \(380 - 300 = 80\) |
The volume is \(80\,\text{cm}^3\).
| \(V\) | \(=\) | \(265 - 250 = 15\) |
The volume is \(15\,\text{cm}^3\).
The cube lifts the level by its own volume.
| \(400 + 45\) | \(=\) | \(445\) |
The new level is \(445\) mL.
The after reading is always larger.
| \(V\) | \(=\) | second \(-\) first |
Subtract the before reading from the after reading.
Common pitfalls
Frequently asked questions
Why does the water level rise?
A solid that sinks takes up space under the surface and pushes that much water aside. The water has nowhere to go but up, so the level rises by the object's volume.
How do I find the volume from the two readings?
Subtract the before reading from the after reading. For example \(380 - 300 = 80\), so the volume is \(80\,\text{cm}^3\).
Why is the answer in cubic centimetres, not millilitres?
The question asks for a volume, so the unit is \(\text{cm}^3\). The number does not change, because \(1\) mL of water fills exactly \(1\,\text{cm}^3\).
What if the object floats?
Displacement only works when the object sinks and is fully under the water. A floating object does not push aside its whole volume.
Can I use displacement for a shape a ruler could measure?
You can, but it is mostly used for irregular shapes like a rock or a key, where length \(\times\) width \(\times\) height will not work.