Overview
-
Equations of 3DShapes
-
Circle Theorems
-
3D Pythagoras Theorem
Equations of 3D Shapes
We need to know the volume and surface area equations of 3D these 3D shapes:
1. Cylinders
2. Spheres
3. Cones
Circle Theorems
3D Pythagoras Theorem
How to carry out Pythagoras' theorem on a 3D shape
-
In order to do this, we need to do regular Pythagoras' theorem twice
-
For example
-
We need to start by drawing a right angle triangle inside the cuboid with the hypotenuse as the diagonal
-
We know that the height of this right angled triangle is 3 and we need to find the length of the base of the triangle in order to find the length of the diagonal
-
In order to find the base we create another right angled triangle and use Pythagoras' Theorem, with the length and height of the cuboid
-
Therefore we know our base length is √160
-
Now we use Pythagoras' Theorem again on the other right angled triangle with our diagonal as the hypotenuse
-
Therefore our length between the diagonals is 13
Practice Question:
Solution:
