Volume of Prisms and Capacity

In short: The volume of a prism is the area of its end times its length, so a box is length × width × height. One cubic centimetre holds 1 mL, so 1000 cm³ is 1 litre. When water rises in a tank, the extra volume is the base area times the rise.

Before you start

• Area of rectangles and triangles, and volume of a box (see Perimeter, Area and Volume).
• Changing mL to L (see Metric Units and Conversions).

Volume of a prism

A prism has the same shape all the way along (see 3D Shapes, Nets and Views). Its volume is the area of that shape times the length.

A cylinder

A cylinder is like a prism with a circle for its end. The area of a circle is $\pi \times r\times r$, where $r$ is the radius and $\pi$ is about 3.14.

Volume and capacity

Capacity is how much a container holds. The units fit together:

Water that rises

Quick summary

• Volume of a prism $=$ area of the end $\times$ length.
• A box: $l\times w\times h$. A cylinder: $3.14\times r\times r\times h$.
• 1 cm³ holds 1 mL, 1000 cm³ holds 1 L, and 1 m³ holds 1000 L.
• Water rise $=$ volume added $÷$ base area.
• An object's volume equals the volume of water it pushes up.
• Doubling every edge makes the volume 8 times bigger.

Quiz