Surface Area and Volume

Colourful Cube

Stage: 3 Challenge Level: Challenge Level:1

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: Challenge Level:2 Challenge Level:2

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: Challenge Level:2 Challenge Level:2

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: Challenge Level:2 Challenge Level:2

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.

Cuboids

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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?

Efficient Cutting

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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: Challenge Level:3 Challenge Level:3 Challenge Level:3

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: Challenge Level:3 Challenge Level:3 Challenge Level:3

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