Ball Packing

If a ball is rolled into the corner of a room how far is its centre from the corner?

Three Balls

A circle has centre O and angle POR = angle QOR. Construct tangents at P and Q meeting at T. Draw a circle with diameter OT. Do P and Q lie inside, or on, or outside this circle?

In a Spin

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

Fill Me up Too

Age 14 to 16Challenge Level

Imagine a conical container that contains a volume of 10cm$^3$ when filled to a height of 1cm:

 Height Volume 1 10 2 80 3 270

What is the relationship between the height and volume as this cone is filled?
How could you draw a graph to show this?