(1/3) x base x height of the pyramid.
There is another way to show the same result. This approach involves dividing a cube into 6 square pyramids. How we do this is to draw a line from every vertex to the vertex diagonally opposite. Connecting the four vertexes together, you will get 6 square pyramids as show in the picture below.
height of cube = 2 x height of square pyramid
base of the cube = base of the square pyramid
Based on the information above we can arrive at this expression:
Volume of square pyramid
= (length of cube x breadth of cube x height of cube) ÷ 6
= [length of cube x breadth of cube x (2 x height of square pyramid)] ÷ 6
= (1/3) x base of cube x height of pyramid
= (1/3) x base of square pyramid x height of square pyramid
This can be easily seen in the animation below.
Cheers,
Group F
Group F
The prove is really awesome! It's an alternative systematic way of deriving the formula for pyramid. In the previous proof, students were asked to cut out 3 pyramids to assemble them to form a cube. However, in the above proof, students can explore how to cut the cube into six equal square pyramids. In this way, students will be able to see the formula unfold before their eyes. This is truly amazing and it will be a Eureka! moment for them. In addition, students will be able to derive the formula for the volume the pyramid using the volume of the cube. It can be designed as a self-discovery activity for students to stimulate their inquisitive minds! Cool stuff and Two thumbs up! :)
ReplyDeleteCheers,
Matthias Low
There's a difference. This proof is for right square pyramid, whereas the previous proof is for any square pyramid.
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