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