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.
Which of these infinitely deep vessels will eventually full up?
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?
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?
If the radius of the tubing used to make this stand is r cm, what is the volume of tubing used?
Analyse these beautiful biological images and attempt to rank them in size order.
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. . . .
Can you work out the dimensions of the three cubes?
Imagine different shaped vessels being filled. Can you work out
what the graphs of the water level should look like?
Various solids are lowered into a beaker of water. How does the
water level rise in each case?
Can you choose your units so that a cube has the same numerical value for it volume, surface area and total edge length?
Can you draw the height-time chart as this complicated vessel fills
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.
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.
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?
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 ?
An aluminium can contains 330 ml of cola. If the can's diameter is
6 cm what is the can's height?
What is the volume of the solid formed by rotating this right
angled triangle about the hypotenuse?
Practice your skills of measurement and estimation using this interactive measurement tool based around fascinating images from biology.