 # How do you calculate the volume of a pizza?

28th October, 2021

## Have you ever wondered how to calculate the volume of a pizza?!

Hint is in the picture….

(full explanation follows later)

It is basically the same as working out the volume of a cylinder, but with a side-order of fun. Before we get on to the solution for this, let’s look at some simpler questions…

## How to calculate the volume of a cuboid?

A typical maths exam question – calculate the volume of this cuboid (basically a box shape). How about a more interesting question?

### How to calculate the volume of a Rubik’s cube? (Ok, it’s a cube rather than a cuboid, but it happens to be a cuboid with sides all the same length)

Another way of thinking of it….” How many smaller cubes are there within this one cube?” (assuming it is made up of small cubes all the way through and cannot be twisted like a real Rubik’s cube)

The number of small cubes on the front face is 3 x 3 = 9 (the length x width) – think of this as a “slice”

The number of “slices” is 3, therefore the total number of small cubes is 9 x 3 = 27

### Volume of a cuboid = width x height x length

To sum up, the volume of the cube can be calculated in one line: 3 x 3 x 3 = 27

(And the answer to the above exam question is 2 x 3 x 9 = 54cm³)

## How to calculate the volume of a triangular prism?

Another typical maths exam question – calculate the volume of this triangular prism Let’s find a more interesting way to look at this… Who doesn’t love chocolate?

### How to calculate the volume of a Toblerone? This particular chocolate comes in a distinctive box, which just happens to be a triangular prism. The box is 6cm wide, 5cm tall and 30cm long

Volume of a prism is the area of a “slice” of the cross-section, multiplied by how deep / long / tall it is.

This time the “slice” is a triangle.

The area of a triangle is ½ x base x height

Then multiply this by the length.

### Volume of a triangular prism = ½ x base x height x length

Therefore, the volume of the Toblerone is ½ x 6 x 5 x 30 = 450cm³

(And the answer to the above exam question is ½ x 5 x 4 x 12 = 120cm³)

## How to calculate the volume of a cylinder?

A classic maths paper question is this – calculate the volume of this cylinder ### How to calculate the volume of a tin of Heinz baked beans? It’s a circular prism, but with its own special name, “cylinder”. This tin is 10cm tall with a radius of 3.5cm

As mentioned before, the volume of a prism is the area of a “slice” of the cross-section, multiplied by how deep / long / tall it is.

This time the “slice” is the area of a circle.

Area of a circle is π x r²  (Look here if not sure how to calculate the area of a circle)

Then multiply this by the height.

### Volume of a cylinder = π x r² x height

Therefore, the volume of the tin of beans is π x 3.5² x 10 = 385cm³ (to 3 significant figures)

(And the answer to the above exam question is π x 2² x 5 = 63cm³ (to 2 significant figures))

## And so… how to calculate the volume of a pizza?

If we label the radius (the length from the centre to the edge of the pizza) as ‘z’

And we label the height as ‘a’

Using the formula

### Volume of a cylinder = π x r² x height … it is Pi x z² x a   = Pi . z . z . a = Pizza! 😊

(Yep, how cheesy is that?!)

I’m still peckish… who wants to find out how to find the volume of an orange? Or Terry’s chocolate orange?