Volumes of Complex Shapes

We are now spending some time looking at the volumes of complex shapes. These are shapes that do not have a constant profile through them. The shapes we are looking at will be pyramids, cones, and spheres.

Pyramids
The volume of a pyramid can be found using the following formula;

An example of using this would be; 

Cone

The volume of a cone can be found using the following formula; 

An example of using this would be; 

Sphere

The volume of a sphere can be found using the following formula; 

An example of using this would be; 

So these formula's are quite easy to use (as you can see from the examples above). With the cones and pyramids, if you do not know a dimension that you may need for the problem (i.e. the height of the shape) you will need to use Pythagoras' Theorem to work that out. If you do not remember how to do this, have a look back at some previous posts because it is used a lot in some of those. 

You should now be able to finish the worksheet on the surface area and volumes of complex shape. There will be a test soon, but I will keep you posted on that. 

As always, feel free to comment on this post if you have any questions, or email or chat to me in person.