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Daily Math Minute

Measurement & Data

Volume of Rectangular Prisms

Finding volume using the formula V = l × w × h.

Intermediate20 min lesson3 min readUpdated August 12, 2026Author not yet attributed

Prerequisites

  • Understanding Volume

A Formula for Volume

In the last lesson, volume came from multiplying one layer's cube count by the number of layers. Before reading on, try to predict a formula: if a box has a length, a width, and a height, how do you think those three measurements combine to give the volume?

One layer's cube count is really just the area of the box's base — length times width, the same formula from Grade 3. Stacking that base layer once for every unit of height means multiplying by the height too. That gives volume as length times width times height, for any right rectangular prism.

V=l×w×hV = l \times w \times h

Worked Example — Finding Volume with the Formula

A box has a length of 8 units, a width of 5 units, and a height of 3 units. What is its volume? Multiply all three dimensions: 8 × 5 × 3 = 120. The volume is 120 cubic units.

Worked Example — Finding a Missing Dimension

A box has a volume of 90 cubic units, a length of 6 units, and a width of 5 units. What is its height? Since volume equals length times width times height, first find the base area: 6 × 5 = 30. Then divide the volume by that base area to find the height: 90 ÷ 30 = 3. The height is 3 units.

Geometry Canvas

Construct
Objects
  1. 1.

    P1: a free point, draggable on the plane

  2. 2.

    P2: a free point, draggable on the plane

  3. 3.

    P3: a free point, draggable on the plane

  4. 4.

    poly1: the polygon through P1, P2, P3

Measurements
  • poly1area = 15perimeter = 17.66

Tip

Check that a volume formula answer is reasonable by comparing it to the base area alone — the volume should always be larger than the base area whenever the height is more than 1 unit, since it's the base area repeated for every layer.

Common Mistakes

  • Adding the three dimensions together instead of multiplying them, confusing volume with a simpler total.

    Volume comes from multiplying all three dimensions together, not adding them — multiplying accounts for every layer of cubes stacked on top of the base.

  • Forgetting to divide by both other dimensions when solving for a missing one, dividing by only one of them.

    To find a missing dimension, first multiply the two known dimensions together to get one combined value, then divide the volume by that combined value.

Key Takeaways

  • The volume of a right rectangular prism equals length times width times height.
  • This formula comes directly from multiplying a base layer's area by the number of layers stacked to reach the height.
  • A missing dimension can be found by dividing the volume by the product of the two known dimensions.

Summary

The volume formula turns the layer-by-layer counting from the last lesson into one fast calculation. The final unit shifts from measuring solids to a new way of locating points — the coordinate plane.

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