AustraliaNSW
Stage 5.1-3

# 7.04 Volume of prisms and cylinders

Lesson

We can find the volume of any prism by multiplying the base area by the height of the prism, where the height of the prism is the distance between the two base faces.

Volume of a prism

$V=Ah$V=Ah

Where $A$A is the base area and $h$h is the height of the prism.

We can find the volume of a cylinder using the same method, by multiplying the area of the circular base by the height of the cylinder.

Since the area of a circle is given by the formula $A=\pi r^2$A=πr2, the formula for the volume of a cylinder is:

Volume of a cylinder

$V=\pi r^2h$V=πr2h

Where $r$r is the radius and $h$h is the height of the cylinder.

#### Practice questions

##### Question 1

Find the volume of the triangular prism shown.

##### Question 2

A prism has a volume of $1080$1080 cm3.

If it has a base area of $120$120 cm2, find the height of the prism.

##### Question 3

Calculate the volume of the solid. Assume that the solid is a quarter of a cylinder.

##### Question 4

A wedding cake with three tiers rests on a table. The layers have radii of $50$50 cm, $54$54 cm and $58$58 cm, as shown in the figure. If each layer is $21$21 cm high, calculate the total volume of the cake in cubic metres.

### Outcomes

#### MA5.2-11MG

calculates the surface areas of right prisms, cylinders and related composite solids

#### MA5.2-12MG

applies formulas to calculate the volumes of composite solids composed of right prisms and cylinders