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# Volumes (A Comparison)

Now we’re up to volumes on a worksheet page two. And they appear in column A and we have the length of the side of each of our solids. Now I’ve given you some formulas, and you can work out the volume of each. So this will be a matter of substituting those values into the formulas to see what we get. I’m going to make the cube one, so it’s easy to compare the other volumes to the cube. The next solid to look at would be the tetrahedron inscribed in the cube. And there’s the formula. And I’ll give you 30 seconds to do the substitution. Well, the answer is a third of a cubic unit. Already we’ve learned a tetrahedron inscribed in a cube is exactly one third. Its volume. The next solid would be the octahedron inscribed in the tetrahedron, there is the formula 30 seconds and that is one sixth of a cubic unit. one sixth, the volume of the cube and one half the volume of the tetrahedron the next solid would be The icosahedron and for this formula, you had better use your calculator and it’s 0.12 cubic units to two decimal places. And finally, the dodecahedron there’s the formula. And again, you’d better use your calculator That’s 1.81 cubic units. That completes each of the volumes for our platonic solids. If we compare the volumes, we might find something interesting. And it’s in these three, that it’s the most interesting. The tetrahedron inscribed in the cube is exactly a third its volume. And the octahedron is half that again. And he’s there for me. one sixth of a cube. So that’s the volumes covered. In the next video, I want to look at something called duality in platonic solids. Before in the video after that, we study the surface areas