Introduction to Complex Shapes

We are now moving on from basic prisms to complex prisms and shapes. Complex prisms are prisms that do not have a constant profile through them. The complex shapes we will be looking at are cones, pyramids, and spheres.

Before we find surface areas and volumes, we need to know how to find essential information about these shapes. When dealing with cones and pyramids, we need to know how to find the slant height, the height, and also information about the base (either the radius of the base in the case of a cone, or the dimensions of the base in the case of a pyramid).

To find this information, we need to use Pythagoras' Theorem.

For example, we may have a cone like this;

We know the height, and we also know the radius of the base, but we don't know the slant height. We can use Pythagoras' Theorem to find this. Remember that Pythagoras' Theorem is; 

We need to remember that the value for "c" is always the length of the longest side of the triangle. "a" and "b" are the lengths of the other two sides. 

So going back to our cone above, we can make a right angled triangle using the height and the radius to find the slant height. It would look like this; 

Using Pythagoras' Theorem we can substitute in the values of 15 for "a" and 8 for "b" and use this to solve for the unknown side like so; 

So we have now found that the slant height is 17cm.

We can use Pythagoras' Theorem and a similar method to find out the height of the cone or the radius of the cone as well if either of these are unknown. 

If you are still struggling with using Pythagoras' Theorem, have a look at this website; 

http://www.mathsisfun.com/pythagoras.html

I have uploaded a new worksheet into the "Work Sheets" tab. You should be able to work through at least the first page of this. The second page has work on Pyramids, and the method is very much the same for these. 

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