Volume of rectangular prisms (grade 5) · lesson

Length × width × height

💡 The volume of a box is length times width times height, in cubic units.

Multiply all three edges of the box. The answer is in cubic units, like cubic cm.

A cube has all edges the same. A cube with 4-inch edges has a volume of 4 × 4 × 4 = 64 cubic inches.

🧠 Let's work it out

A box is 7 cm long, 2 cm wide, and 3 cm tall. What is its volume?

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💡 Find how many cubes fit in one layer, then multiply by the number of layers.

The bottom layer of a box is a rectangle of cubes. Length × width gives the cubes in it.

Stack the layers up to the height. If the cubes are bigger than 1 unit, first find how many fit along each edge.

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How many 2-cm cubes fit in a box 8 cm by 4 cm by 6 cm?

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💡 If you know the area of the base, multiply it by the height to get the volume.

The base area tells how many cubes cover the bottom. The height tells how many layers.

So volume = base area × height.

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A box has a base area of 25 square inches. It is 3 inches tall. What is its volume?

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💡 Divide the volume by the base area to find the height.

Volume = base area × height. So if you know the volume, work backward.

First find the base area. Then divide the volume by it.

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A box has a volume of 56 cubic feet. Its base is 4 ft by 2 ft. How tall is it?

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💡 To find the volume of two boxes together, find each volume and add them.

Volume adds up. Two boxes together take up the space of both.

Find each volume on its own. Then add them.

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One box is 2 by 2 by 3. Another is 3 by 3 by 1. What is their total volume?

What do you think comes next?