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Math · Grade 6 Math

Chapter 8: Volume with Fractional Edges

Finding a Missing Edge

Working backwards from the volume.

Lesson
3
Time
About 17 minutes
0 of 7 done

Step 1: Let's Learn

Read it, or press Listen and follow the words.

Volume is length × width × height. Knowing three of those four lets you find the fourth.

Work out the base first

Multiply the two edges you know. That gives the area of one face.

Then divide

Volume ÷ base area = the missing edge.

Check by multiplying back

Put the answer in and multiply all three. The original volume should return.

Divide to work backwards

If a box has volume 24 cubic units, length 4 and width 3, then the height is 24 ÷ (4 × 3) = 2. Divide the volume by the product of the two known edges. Formulas run in both directions.

Think of it as base area first

The base area is 4 × 3 = 12, and volume is base area × height, so height is 24 ÷ 12 = 2. Working through the base area is one division instead of two and generalises to prisms whose base is not a rectangle.

Multiply back to check

4 × 3 × 2 = 24, matching the given volume. Multiplying back is quick and independent of how you found the missing edge. Get into the habit — it will still be the right check when the formulas get more complicated.

Watch the units

Volume in cubic centimetres divided by an area in square centimetres gives a length in centimetres. The units work out correctly, and if they do not, you divided by the wrong thing. Unit tracking is a genuine error check, not bookkeeping.

Step 2: Try It Yourself

Tap and try it out.

Change the edges and watch the volume follow.
  • Cubes in one layer4 × 3 = 12
  • Layers2
  • 4 × 3 × 224 cubic units

Counting every cube gives 24, and so does 4 × 3 × 2. The formula is a shortcut for the count.

Step 3: Watch an Example

One step at a time.

Watch Ana Find a Height

A box has volume 60, length 5 and width 3.

  1. Step 1

    She multiplies the two known edges: 5 × 3 = 15.

Step 4: Your Turn

Practice makes it stick.

The Tank

Problem 1 of 2

Volume 48, length 4, width 3. What is the height?

The Crate

Problem 2 of 2

Volume 90, length 5, height 3. What is the width?

Work It Backwards

1 of 4

Volume 24, base area 6. Missing edge?

2 of 4

Volume 100, length 5, width 4. Height?

3 of 4

Volume 36, length 3, height 3. Width?

4 of 4

Volume 2 by 3 by 7. What is it?

Step 5: Quick Check

Show what you know.

Question 1 of 1

Volume 72, length 6, width 3. Height?

What You Learned

  • Volume is the three edges multiplied together.
  • Multiply the two known edges, then divide the volume by that.
  • Check by multiplying all three back to the original volume.