Volume
In short: Volume tells how much room a 3D object takes up or holds, counted in cubic units, so a box 5 long, 3 wide and 4 tall fits 60 unit cubes.
6th GradeGeometry6.G.A.2
What is Volume?
Fill a tank with water, a truck with sand or a room with air: the volume says how much it takes. You can find it by packing unit cubes inside and counting them layer by layer.
Units are cubic centimeters, cubic feet and the like. For a box with length \(\ell\), width \(w\) and height \(h\), \(V = \ell w h\), which is the base layer times the number of layers.
How to spot it
- A question asks how much a tank, box, pool or container can hold.
- A picture shows a block made of stacked cubes or layers.
- The answer must be in cubic units such as cm³ or cubic feet.
- A capacity word like liters or gallons appears and you need a space measure from lengths.
The method
- Find the area of the base layer: length times width.
- Count how many layers stack up by reading the height.
- Multiply layer size by the number of layers: \(V = \ell w h\).
- Write the result in cubic units and check the size is sensible.
Volume: solved example
Problem
An aquarium at a Chicago school is 24 inches long, 12 inches wide and 16 inches tall. What is the greatest volume of water it can hold?
Solution
Base layer: \(24 \cdot 12 = 288\) square inches. Height: 16 inches.
\(V = 288 \cdot 16 = 4{,}608\). The tank holds 4,608 cubic inches of water.
Try it
Question 1
A crate measures 3 feet, 2 feet and 1.5 feet on its edges. How much can it hold?
Show the answer
\(3 \cdot 2 \cdot 1.5 = 9\) cubic feet.
Question 2
A cube has edges of 7 cm. How many cubic centimeters does it hold?
Show the answer
\(7 \cdot 7 \cdot 7 = 343\) cm³.
Volume vs. Surface Area
Surface area is the wrapping paper that covers a solid’s outside, in square units. This measure is what fits inside, in cubic units. A bigger wrapper does not always mean a bigger inside.
Keep going
Lessons
Worksheets and quizzes
Related words
Whole dictionary: A–Z · 6th Grade · Geometry