### In a Spin

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

### Conical Bottle

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?

### Peeling the Apple or the Cone That Lost Its Head

How much peel does an apple have?

# Fill Me up Too

##### Stage: 4 Challenge 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?