Neft Teacher · Learn It

Unit 5 · Standard 6.GR.2

Volume of Rectangular Prisms

Lesson 5-10 · Learn It — how the math works

Why we're learning this

Your class is building a time capsule to bury on school grounds. The capsule is a rectangular prism that is 2 feet long, 1.5 feet wide, and 1 foot tall. You need to figure out how much stuff can fit inside — that means calculating the volume!

✱ Math Workbench

Learn It

How do we find volume when an edge is a fraction?

Volume is the space inside a rectangular prism. There are two ways to write the same rule. You can multiply all three edges, V = length × width × height. Or you can find the base area first, B = length × width, and then stack that base up the height: V = B × h. Both give the same number, and both work when an edge is a fraction or a decimal.

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

A classmate asks whether a cube is always a rectangular prism. This prism is built from small cubes that are each ½ inch on every edge.
Where you see this in real lifeA classmate asks whether a cube is always a rectangular prism. This prism is built from small cubes that are each ½ inch on every edge.

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

The problem looks like this
A rectangular box 2 ft long, 1.5 ft wide, and 1 ft tall. length = 2 ft height = 1 ft width = 1.5 ft
  1. My capsule is 2 ft long, 1.5 ft wide, and 1 ft tall. I write V = length × width × height.
  2. I put in the numbers:V = 2 × 1.5 × 1
  3. First I multiply 2 × 1.5 = 3.2 × 1.5 = 3
  4. Then 3 × 1 = 3.3 × 1 = 3
  5. So the is 3 ft³. A fractional edge like 1.5 did not change my steps at all.

Watch out — mistakes students make here

  • Are you adding the dimensions? Volume multiplies all edges: length × width × height.
  • Check the units. Area is square units (²), volume is cubic units (³).
  • Recheck which box's volume is larger — recalculate both totals before comparing.

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

Same steps, new numbers.

  1. Now try a box that is 4 long, 2 wide, and 0.5 tall. Let's do it the base-area way. What is the base, 4 × 2?base, 4 × 2
  2. The is B = 8. Picture that base sitting on the table — that is one layer.
  3. Now stack the base up the height: V = B × h = 8 × 0.5 (that means half of 8). What is the ?V = B × h = 8 × 0.5
  4. Yes, V = 4 . Check it the other way: 4 × 2 × 0.5 = 4. Same answer, because B × h already used the length and width.4 × 2 × 0.5 = 4

On your ownYou do — solve this one by yourself

Before you start, remember:

  • In the table below, find the of each capsule design. Use whichever form you like: V = l × w × h, or find the first and multiply by the height.
  • Some edges are fractions or decimals — use the same steps and write your answer in ft³.

Solve: Find the missing dimension or for each container.

ContainerLengthWidthHeightVolume
Box A12 in5 in3 in
Box B7 cm4 cm168 cm³
Box C8 ft5 ft240 ft³

Stuck? Open one hint at a time.

Hint 1

Check each row: Box A is missing its volume, but Boxes B and C are each missing one dimension.

Hint 2

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

Hint 3

Box B: multiply the known edges 7 × 4 = 28, then ask what number times 28 makes 168.

Check my answer
✅ Answers:
  • Box A → Volume: 180 in³
  • Box B → Width: 6 cm
  • Box C → Length: 6 ft
Box A is missing its volume, so multiply all three edges: 12 × 5 × 3 = 180 in³. Boxes B and C are missing an edge, so you divide instead: 168 ÷ (7 × 4) = 168 ÷ 28 = 6 cm for Box B, and 240 ÷ (8 × 5) = 240 ÷ 40 = 6 ft for Box C.

Turn & TalkSay it out loud with a partner

Your time capsule is 2 ft long, 1.5 ft wide, and 1 ft tall — one edge is a fraction. Does having a fractional edge change how you find the ? Why or why not?

Try starting with:

  • A fractional edge ___ change the method because I still multiply ___ × ___ × ___.Una arista fraccionaria ___ cambia el método porque sigo multiplicando ___ × ___ × ___.
  • The volume of the capsule is ___ ft³.El volumen de la cápsula es ___ ft³.
Use these wordsvolumedimensionsrectangular prismbase areacubic units