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Volume: cheat sheet

Area, volume, circles and Pythagoras · The words and methods from the lessons, with an example of each.

volume of a prism

Each layer is the base (the cross-section); the height counts the layers. For a box, V=l×w×hV = l \times w \times h.

V=A×hV = A \times h
A 4 by 3 by 5 box in layers of 12 cubes
A 4 by 3 by 5 box in layers of 12 cubes

volume and capacity

A cubic metre is 100 × 100 × 100 = 1 000 000 cm³: convert each of the three lengths.

1 cm3=1 mL,1000 cm3=1 L,1 m3=1000 L1\ \text{cm}^3 = 1\ \text{mL}, \quad 1000\ \text{cm}^3 = 1\ \text{L}, \quad 1\ \text{m}^3 = 1000\ \text{L}

cross-section

The shape that is the same all the way along a prism, like a slice of bread. A triangular prism's cross-section is a triangle: halve first.

V=12×6×4×10=120 cm3V = \tfrac{1}{2} \times 6 \times 4 \times 10 = 120 \text{ cm}^3
A triangular prism, half of a 4 by 3 box, 5 layers high
A triangular prism, half of a 4 by 3 box, 5 layers high

capacity

How much a container holds. A 10 cm cube holds 1 litre.

1 cm3=1 mL1000 cm3=1 L1 \text{ cm}^3 = 1 \text{ mL} \qquad 1000 \text{ cm}^3 = 1 \text{ L}

volume of a prism

The area of the end times the length, for any right prism. Divide to find a missing length.

V=Ahh=V÷AV = A h \qquad h = V \div A
The board