Surface Area and Volume

Painted Cube

Stage: 3 Challenge Level: Challenge Level:1

Imagine a large cube made from small red cubes being dropped into a pot of yellow paint. How many of the small cubes will have yellow paint on their faces?

Cuboid Challenge

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

What size square corners should be cut from a square piece of paper to make a box with the largest possible volume?

Changing Areas, Changing Volumes

Stage: 4 Challenge Level: Challenge Level:1

How can you change the surface area of a cuboid but keep its volume the same? How can you change the volume but keep the surface area the same?