Depth · one concept from first principles · step 2 of 4

A submerged stone displaces its own volume

A tank shaped like a rectangular prism holds water, as shown at the right. When a stone is placed in it so that the stone is completely under water, the water rises to a height of $30\ \text{cm}$ . What is the volume of the stone, in $\text{cm}^3$ ? (Ignore the thickness of the tank.)

Geometry

Your answer

How to solve

Strategy Draw a Diagram — The stone's own shape is unknowable and does not matter. What matters is that it takes up room the water used to have, so the water it pushed up is the same size as the stone -- and that pushed-up water is a neat rectangular slab.

1STEP 1

Find how far the water rose

Subtract the old height from the new one.

30 - 25 = 5

2STEP 2

See that slab of water as the stone

No water was added, so the stone pushed that much water upward. The stone takes up exactly the room that slab of water now occupies.

3STEP 3

Measure that layer

The layer fills the whole floor of the tank and is 5 cm thick.

20 × 16 × 5 = 1600

Answer

1600 cm³

Compare the two water volumes: 20 × 16 × 25 = 8000 before and 20 × 16 × 30 = 9600 after -- a difference of 1600 cm³, and no water was added.

Takeaway

A sunk object pushes up its own volume of water -- so measure the water instead of the object.

Find how far the water rose
See that slab of water as the stone
Measure that layer

Where next?

Another one like thissuggested

12 practice problems

Step back and solidifysuggested

Build the prism from its top, front and side views Volume needs every length in the same unit

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▶ Practice — 12 problems