math · 32 minutes · Official OETT Aligned
Volume: Space Inside a Shape
Boxes, cylinders, and cubic units
What to know
- volume: space an object takes up or holds
- length, width, and height
- cylinder: a shape with circular ends
- cubic feet and cubic yards
Volume tells you how much a tank, box, or other solid shape can hold.
The core rule
Box volume = length × width × height. Use matching units for all measurements.
A cylinder has volume π × radius × radius × height. Use about 3.14 for π. Volume uses cubic units because it measures space in three directions. One cubic yard is 3 feet long, 3 feet wide, and 3 feet high, so it equals 27 cubic feet.
Worked examples
Example 1: easy
A 4×3×2-ft box holds 24 cubic feet.
- Use box volume V = L × W × H.
- Calculate 4 × 3 × 2 = 24 cubic feet.
Volume needs length, width, and height.
Example 2: medium
Two cubic yards equal 54 cubic feet.
- One cubic yard equals 3 × 3 × 3 = 27 cubic feet.
- Multiply 2 × 27 = 54 cubic feet.
A cubic yard is 3 feet in each of three directions.
Example 3: hard
A 2-ft-radius, 5-ft-high cylinder holds about 62.8 cubic feet.
- Use cylinder volume V = πr²h with r = 2 ft and h = 5 ft.
- Calculate 3.14 × 2² × 5 = 3.14 × 20 = 62.8 cubic feet.
Multiply the area of the circular base by its height.
Common mistakes
One cubic yard equals three cubic feet.
Multiply in all three directions: 3 × 3 × 3 = 27 cubic feet.
Put it into practice
Use guided explanations, check your answers, and try a new variation.