Volume of 3D Objects

≈ 25 min

The volume of a solid is the amount of space inside it — how much it can hold. For any prism (a solid with the same cross-section all the way through) and for a cylinder:

\text{Volume} = \text{area of base} \times \text{height}

Rectangular prism: $V = l \times w \times h$ .
Cylinder: $V = \pi r^2 \times h$ (the base is a circle of area $\pi r^2$ ).

Worked example. A cylinder with radius 7 cm and height 10 cm, using $\pi = \frac{22}{7}$ : $V = \dfrac{22}{7} \times 7^2 \times 10 = \dfrac{22}{7} \times 49 \times 10 = 22 \times 7 \times 10 = 1540$ cm $^3$ .

Capacity link: $1000$ cm $^3 = 1$ litre, and $1$ m $^3 = 1000$ litres — handy for water tanks.

Find the volume of a rectangular prism measuring $6 \times 5 \times 4$ cm, in cm $^3$ .

The volume of a cylinder (radius $r$ , height $h$ ) is given by…

$\pi r^2 h$

$2\pi r h$

$\frac{1}{3}\pi r^2 h$

$\pi r h^2$

A cylinder has radius 7 cm and height 10 cm. Using $\pi = \frac{22}{7}$ , find its volume in cm $^3$ .

A rectangular water tank is 2 m long, 1 m wide and 0.5 m deep. How many litres of water does it hold when full? (1 m $^3$ = 1000 L)