Task 2 Rational and Irrational Numbers
Part A
The pyramids have always fascinated Kristina, so she wants to build two model pyramids to put on her mantel.
She wants her model of Khufu’s pyramid to have a volume of 73.5 cubic inches and a height of 4.5 inches. What
would the side length of the base of the pyramid be? Is this number rational or irrational? Why?

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Part B
The volume of Khafre’s pyramid is about the volume of Khufu’s pyramid. If Kristina wants to make the
second model pyramid so its volume is the volume of the rst model pyramid, what volume should she
make the second model pyramid?

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Part C
If the height is 4.41 inches and the volume is the volume found in Part B, what will the side length of the
pyramid’s base be? Is the number rational or irrational? Why?

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Part D
For the model to be to scale, the ratio of the height to the side length should be the same for both the actual
pyramid and the model. Is the model of Khufu’s pyramid to scale? If not, is it close?

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Part E
Is the model of Khafre’s pyramid to scale? If not, is it close?