A **prism** is a shape which has the same **cross-section throughout its height.**

This means that if you cut a prism, it will get smaller but the overall shape stays the same.

Here are some examples:

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If you** **sliced through the cross-section of these shapes, they would get smaller but the **overall shape would stay the same**.

Cross-sections of the shapes above would be a circle, rectangle, square and triangle.

The** cross-section **is the **shape of the face **of the prism.

How do we find the volume? They are all different shapes.

Ah yes, yet another formula to learn:

**Volume of a prism = area of the cross-section x height**

Before we continue, we need a recap of how to find the area of these shapes.

**Area of a square = base x height**

**Area of a rectangle = base x height**

**Area of a triangle = base x height ÷ 2**

**Area of a circle = π x r x r**

Can you remember the value of π? Don't worry, you will find out later if you have forgotten.

Almost there. To find the **volume **we calculate the **area of the face **first and then **multiply by the height.**

Time to practise.

Find the volume of this box of chocolates. Base = 6 cm

The face (cross-section) is a **square -** find the area first.

6 x 6 = 36 cm, now just multiply by the length which, as it's a square box , is also 6 cm. 36 x 6 = 216 cm³

Find the volume of the cornflakes box. Base 12 cm, height 6 cm, length 30 cm

The face (cross-section) is a **rectangle** - find the area first.

12 x 6 = 72 cm, now just multiply by the length 72 x 30 = 2160 cm³

Find the volume of the triangular prism. Base 4 cm, height 4 cm, length 12 cm

The face (cross-section) is a **triangle**** **- find the area first.

4 x 4 = 16 ÷ 2 = 8 cm, now just multiply by the length 8 x 12 = 96 cm³

Find the volume of this can. Radius 4 cm, length 8 cm

The face (cross-section) is a **circle** - find the area first.

Did you remember the value of π? Of course, it's **3.142**

Area = 3.142 x 4 x 4 = 50.27

Now multiply by the length 50.27 x 8 = 402.16 cm³

That was a bit of a marathon, wasn't it? Guess what, it is not over...

Activity time!