# Surface Area and Volume

### Colourful Cube

##### Stage: 3 Challenge Level:

A colourful cube is made from little red and yellow cubes. But can you work out how many of each?

### Sending a Parcel

##### Stage: 3 Challenge Level:

What is the greatest volume you can get for a rectangular (cuboid) parcel if the maximum combined length and girth are 2 metres?

### Cuboid Challenge

##### Stage: 3 Challenge Level:

This problem offers opportunities for visualising, and for consolidating the formula for working out the volume of a cuboid.

### Changing Areas, Changing Volumes

##### Stage: 3 Challenge Level:

Working on this problem will give students a deeper understanding of the relationship between volume and surface area, and how they change as the dimensions of a cuboid are altered.

### Efficient Cutting

##### Stage: 3 Challenge Level:

This problem offers an opportunity for students to apply their knowledge of areas and circumferences of circles, and volumes of cylinders.

### Cola Can

##### Stage: 3 Challenge Level:

An aluminium can contains 330 ml of cola. If the can's diameter is 6 cm what is the can's height?

### Painted Cube

##### Stage: 3 Challenge Level:

Exploring a variety of painted cubes may produce patterns which students can describe spatially, numerically and algebraically.

### Cuboids

##### Stage: 3 Challenge Level:

Find a cuboid (with edges of integer values) that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?