a Draw different diagrams of the pyramid's base, increasing the number of the base's sides. What figure does the base remind you of?
B
b Draw different diagrams of the prism's base, increasing the number of the base's sides. What figure does the base remind you of?
A
a A cone.
B
b A cylinder.
Practice makes perfect
a We need to analyze how the base of the pyramid changes as the number of the base's sides increase. Let's start with a base that has 4 sides. Since we are told that the base is a regular polygon, if it has 4 sides, then it is a square.
Let's now increase the number of sides to 8. A regular polygon with 8 sides is an octagon.
Now, we can draw the base with 20 sides and see what we get.
As the number of the base's sides increases, the base becomes more and more similar to a circle. Therefore, continuing the pattern infinitely, the base of the polygon will become a circle. If we draw a triangular faces of the pyramid with base that has 20 sides, the surface will remind us of the curved surface of a cone.
We can conclude that if the number of sides of a pyramid's base increases infinitely, the pyramid will transform into a cone.
b In the case of a prism, the solution is very similar.By increasing the number of the base's sides infinitely, both bases of the prism will become circles. What about the rectangular faces that connect those bases? Let's draw a prism, whose bases have 16 sides each.
As we can see, the rectangular faces are very narrow. As the number of the base's sides increases, they will become more and more narrow, reminding us of the surface of a cylinder. Therefore, by increasing the number of sides of a prism's bases infinitely, the prism will transform into a cylinder.
