Volume of cuboids
Find the volume of right rectangular prisms by packing with unit cubes and show it equals l × w × h (or base area × height); apply V = l × w × h and V = B × h to solve real-world problems; calculate, estimate, and compare volumes of cubes and cuboids in standard units (cm³, m³)
What a learner can do afterwards
- Use V = l × w × h to find the volume of a cuboid 4 cm × 3 cm × 5 cm = 60 cm³
- Explain why packing a prism with unit cubes gives the same result as multiplying edge lengths
- Compare volumes of two cuboids and identify which has greater capacity
1 · Read
You already know how to fill a box with unit cubes and count them. There is a faster way. For a box shaped like a rectangle (a cuboid), multiply the length, the width, and the height to tell fast which box holds more: V = l × w × h.
A box is 4 cm long, 3 cm wide, and 5 cm tall. Multiply the three numbers: 4 × 3 × 5 = 60. The volume is 60 cm³.
Packing cubes one by one gives the same answer as multiplying, because each layer holds l × w cubes and there are h layers stacked up. If you already know the area of the base, call it B, you can use V = B × h instead. For small things use cm³. For very large things, like a swimming pool, use m³.
Box A is 30 cm long, 20 cm wide, 25 cm tall: 30 × 20 × 25 = 15,000 cm³. Box B is 25 cm long, 25 cm wide, 20 cm tall: 25 × 25 × 20 = 12,500 cm³. Box A holds more.
Multiply length × width × height, or base area × height, to find a box's volume in cubic units like cm³ or m³.
More to read
3D Shapes: Geometry Guide For Kids or Math Learners
Boxes, balls, and cans are 3D shapes: they take up space. A cuboid has 6 flat faces, all rectangles. A cube is a special cuboid with all edges equal. Volume is the space inside. For a cuboid, multiply the three edges: a 4 by 3 by 5 box holds 4 x 3 x 5 = 60 unit cubes. Surface area is different: it adds up all six faces and uses square units.
10.7 Volume and Surface Area
Volume fills space, so it comes in cubic units. A sugar cube is about 1 cubic centimetre; a bedroom is measured in cubic metres. For right prisms, volume is base area x height. A pool with base 20 square metres and depth 2 m holds 20 x 2 = 40 cubic metres. Surface area instead adds the faces: it tells you how much paint covers the outside. One fills, one covers.
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Where this leads
16 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.