Perimeter, Area and Volume

Isometric Areas explored areas of parallelograms in triangular units. Here we explore areas of triangles...

Can you maximise the area available to a grazing goat?

Explore the area of families of parallelograms and triangles. Can you find rules to work out the areas?

If you move the tiles around, can you make squares with different coloured edges?

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

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?

Can you find a cuboid that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?

Use a single sheet of A4 paper and make a cylinder having the greatest possible volume. The cylinder must be closed off by a circle at each end.

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

What's the largest volume of box you can make from a square of paper?