P is the midpoint of an edge of a cube and Q divides another edge in the ratio 1 to 4. Find the ratio of the volumes of the two pieces of the cube cut by a plane through PQ and a vertex.

A right circular cone is filled with liquid to a depth of half its vertical height. The cone is inverted. How high up the vertical height of the cone will the liquid rise?

If the radius of the tubing used to make this stand is r cm, what is the volume of tubing used?

The builders have dug a hole in the ground to be filled with concrete for the foundations of our garage. How many cubic metres of ready-mix concrete should the builders order to fill this hole to. . . .

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?

It is known that the area of the largest equilateral triangular section of a cube is 140sq cm. What is the side length of the cube? The distances between the centres of two adjacent faces of. . . .

Analyse these beautiful biological images and attempt to rank them in size order.

Can you choose your units so that a cube has the same numerical value for it volume, surface area and total edge length?

Various solids are lowered into a beaker of water. How does the water level rise in each case?

Imagine different shaped vessels being filled. Can you work out what the graphs of the water level should look like?

Can you draw the height-time chart as this complicated vessel fills with water?

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.

Two circles of equal size intersect and the centre of each circle is on the circumference of the other. What is the area of the intersection? Now imagine that the diagram represents two spheres of. . . .

A tetrahedron has two identical equilateral triangles faces, of side length 1 unit. The other two faces are right angled isosceles triangles. Find the exact volume of the tetrahedron.

An irregular tetrahedron has two opposite sides the same length a and the line joining their midpoints is perpendicular to these two edges and is of length b. What is the volume of the tetrahedron?

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

A plastic funnel is used to pour liquids through narrow apertures. What shape funnel would use the least amount of plastic to manufacture for any specific volume ?

What is the volume of the solid formed by rotating this right angled triangle about the hypotenuse?

Imagine two identical cylindrical pipes meeting at right angles and think about the shape of the space which belongs to both pipes. Early Chinese mathematicians call this shape the mouhefanggai.

Practice your skills of measurement and estimation using this interactive measurement tool based around fascinating images from biology.