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Apply the Volume Formula V = l × w × h

Students use the formula V = l × w × h to calculate the volume of right rectangular prisms with whole-number edge lengths. They identify the length, width, and height from a figure or description and substitute into the formula.

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Apply the Volume Formula V = l × w × h

Grade 5 · Volume Formulas and Applications · question 1 of 3

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20 rungs. A star at the top.

5 cm2 cm3 cm

The tile stack has edges marked. Find its volume.

Read the edges.

How it is taught

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Volume of a rectangular prism is length times width times height.

Multiply all three edges.

7 in7 in12 in

Read it: Volume = length × width × height

A box 4 by 2 by 3 holds 4 × 2 = 8 cubes in its bottom layer, and 3 layers: 8 × 3 = 24. So V = l × w × h = 24 cubic units, and V = B × h: the base's area times the height.

  1. Find the base: length × width, 4 × 2 = 8 square units.
  2. Multiply by the height, which counts the layers: 8 × 3 = 24.
  3. For a solid made of two boxes, find each box's volume, then add them.

The base's area is the number of cubes in one layer.

The height is the number of layers, so base × height counts every cube.

Two boxes that do not overlap each fill their own space, so their volumes add.

V = l × w × h = B × h, in cubic units.

Adding the edges, 4 + 2 + 3, instead of multiplying them.

Volume multiplies: 4 × 2 = 8, then 8 × 3 = 24 cubic units.

A box is 8 by 3 by 4. Its volume is ___ cubic units. — 96. The base is 8 × 3 = 24, and 4 layers: 24 × 4 = 96.

5 × 3 × 4 rectangular prism

Look at this box. Today we'll find the volume of a rectangular prism — volume tells us how much space fits inside.

Grade 5 · Find the volume of a rectangular prism

First, the length — how far the box stretches across. This one is five units long.

Next, the width — how far the box goes back. The width is three units.

And the height — how tall the box stands. The height is four units.

To find the volume, we use this formula: V equals length times width times height.

Now substitute the numbers: five times three times four.

Multiply the first two. Five times three is fifteen.

Then fifteen times four. That's sixty.

The volume is sixty cubic units. Great work!

Now you try. Multiply the edges to find how much space fits inside. Type the volume.

What you see

While they climb, your page writes one true line to ask about tonight, and a short note each Sunday.

MayaGrade 3 · Mathematics
Did you know?

A chessboard has 64 squares — share them out between the 8 rows and each row holds exactly 8.

Today’s goal
1 star — one skill mastered, every rung of its ladder climbed
Climbing now
Divide within 100

An example student.

MayaGrade 3 · Mathematics

Maya earned 2 stars this week — Interpret multiplication as equal groups, which took 6 answers over 3 days before its star landed 3 days ago and Multiply by 6, 7, 8 and 9. Next up: Divide within 100.

An example week.

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