Neft Teacher · Learn It

Unit 5 · Standard 6.GR.2

Determine the Volume of Rectangular Prisms

Lesson 5-5 · Learn It — how the math works

Why we're learning this

Your team is building time capsule containers to store class memories. Each container is a rectangular prism, and you need to figure out how much each one can hold. That means calculating the volume using whole number dimensions! Container A is 5 inches long, 3 inches wide, and 4 inches tall. How much can it hold?

✱ Math Workbench

Learn It

How do we find the volume of a box?

Volume is how much space is inside a 3D shape. For a rectangular prism (a box), volume = length × width × height, measured in cubic units.

Picture itSee what the math looks like before you read about it

Two time capsule containers sit side by side. Capsule A is 4 in long, 3 in wide, and 8 in tall. Capsule B is 6 in long, 6 in wide, and 6 in tall. A classmate says Capsule A must hold more because it looks taller.
Where you see this in real lifeTwo time capsule containers sit side by side. Capsule A is 4 in long, 3 in wide, and 8 in tall. Capsule B is 6 in long, 6 in wide, and 6 in tall. A classmate says Capsule A must hold more because it looks taller.

Watch me solve itI do — read one step at a time

The problem looks like this
A rectangular box 6 long, 4 wide, and 3 tall. length = 6 height = 3 width = 4
  1. My time capsule box is 6 long, 4 wide, and 3 tall. I write the formula:V = length × width × height
  2. I put in the numbers:V = 6 × 4 × 3
  3. First I multiply two of them:6 × 4 = 24
  4. Then I multiply by the last one:24 × 3 = 72
  5. So the is 72 . I use cubic units because volume fills space in 3 directions.

Watch out — mistakes students make here

  • Multiply all three edges: 11 × 5 = 55, then 55 × 4 = ?
  • Square inches (in²) measure area, not volume. Volume uses cubic units (in³).
  • Calculate both volumes first: Bin A = 8 × 6 × 5 and Bin B = 9 × 4 × 7.

Try it with meWe do — you answer first, then check

Same steps, new numbers.

  1. Now a smaller box: 5 long, 2 wide, 2 tall. What formula do we use?
  2. Let's put in the numbers: V = 5 × 2 × 2. What is 5 × 2?V = 5 × 2 × 2
  3. We got 10. Now multiply 10 × 2. What is the ?10 × 2
  4. Yes, V = 20 . Don't forget the cubic units!V = 20 cubic units

On your ownYou do — solve this one by yourself

Before you start, remember:

  • In the table below, find the of each container using V = length × width × height.
  • Write your answer in cubic inches (in³).

Solve: Complete the table. Find the missing dimension or for each time capsule.

CapsuleLengthWidthHeightVolume
Capsule X9 in5 in2 in
Capsule Y6 ft4 ft168 ft³
Capsule Z12 cm5 cm360 cm³

Stuck? Open one hint at a time.

Hint 1

Look at what's missing in each row: Capsule X needs its volume, but Y and Z are each missing one edge.

Hint 2

Missing volume? Multiply all three edges. Missing edge? Divide the volume by the product of the two known edges.

Hint 3

Capsule Y: multiply the two known edges 6 × 4 = 24, then ask what number times 24 makes 168.

Check my answer
✅ Answers:
  • Capsule X → Volume: 90 in³
  • Capsule Y → Height: 7 ft
  • Capsule Z → Width: 6 cm
Capsule X has all three edges, so V = 9 × 5 × 2 = 90 in³. Capsules Y and Z give the volume and are missing one edge, so undo the multiplication with division: 168 ÷ (6 × 4) = 168 ÷ 24 = 7 ft, and 360 ÷ (12 × 5) = 360 ÷ 60 = 6 cm.

Turn & TalkSay it out loud with a partner

Your time capsule container is a . To find how much it can hold, why do you need three measurements (length, width, and height) instead of just one or two?

Try starting with:

  • I need three measurements because volume fills space in ___ directions.Necesito tres medidas porque el volumen llena el espacio en ___ direcciones.
  • Length and width alone only give the ___, not the volume.El largo y el ancho solos solo dan el ___, no el volumen.
Use these wordsvolumelengthwidthheightrectangular prism