Fun with Prism | English. We will first try to make a triangular prism from a rectangular block of foam rubber. This 3D structure has 2 same triangles as the base and 3 rectangles on the side. So we make any triangle at one of the base of this. We make same triangle on the other base and then join the point of the triangle with a line. Now we will cut along this line to the two other corners of the cuboids. Here we get the first cut and so we have one rectangular side of the prism. Now we will cut with this along new edge and another side of cuboids to make second rectangular side of prism. One of the sides of cuboids makes the third rectangle and so our triangular is ready. Now we will cut this prism into three triangular pyramids. Triangular pyramids are made of four triangular faces. A triangular base and three triangular faces joining this triangular base. First we will cut along this edge. So we get the first pyramid. And we mark the newly cut triangular face as A. Then we cut along this other edge. This makes second pyramid. And we mark the newly cut triangular faces as B. And the third structure left is the third pyramid. You can see all these pyramids have three triangular faces.
And interestingly all these three pyramids have same volume. Let’s see how. Pyramid 1 and 2 has same base (as the triangle of the prism) and same height. SO pyramid 1 and 2 have same volume. Pyramid 2 and three have same base (marked B) and same height. So pyramid 2 and three have same volume. So all three pyramids have same volume and we can join them so make a triangular prism. Hence we can prove that volume of pyramid is one third of the volume of a prism.
So we can see that volume of prim is base times height and volume of pyramid must be 1/3 base times height since 3 equal volume pyramid make a prism.
A prism of any number of sides can be cut in many triangular prisms this thing holds for any sided prism.
This work is supported by IUCAA (www.iucaa.in) and TATA Trust (www.tata.com/aboutus/sub_index/Tata-trusts)
Credits:,Ashok Rupner, Manish Jain, Pradnya Pujari, Shivaji Mane, Jyoti Hiremath, Arvind Gupta, Vidula Mhaiskar TATA Trust: Education is one of the key focus areas for Tata Trusts, aiming towards enabling access of quality education to the underprivileged population in India. To facilitate quality in teaching and learning of Science education through workshops, capacity building and resource creation, Tata Trusts have been supporting Muktangan Vigyan Shodhika (MVS), IUCAA's Children’s Science Centre, since inception. To know more about other initiatives of Tata Trusts, please visit www.tatatrusts.org
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