story problem

I'm horrible with story problems but this one just kind of confuses me with the wording its something I found on the net can anyone help?


A man has a miniature Pyramid of Egypt. It is 3 inches in height. The man was invited to display it at an exhibition. He felt it was too small and decided to build a scaled-up model of the Pyramid out of material whose density is (1/8) times the density of the material used for the miniature. He did a "back-of-the-envelope" calculation to check whether the model would be big enough.

If the mass (or weight) of the miniature and the scaled-up model are to be the same, how many inches in height will the scaled-up Pyramid? Give your answer to two places of decimal.

Quote:

---

Originally Posted by flyingsilverschoo

I'm horrible with story problems but this one just kind of confuses me with the wording its something I found on the net can anyone help?


A man has a miniature Pyramid of Egypt. It is 3 inches in height. The man was invited to display it at an exhibition. He felt it was too small and decided to build a scaled-up model of the Pyramid out of material whose density is (1/8) times the density of the material used for the miniature. He did a "back-of-the-envelope" calculation to check whether the model would be big enough.

If the mass (or weight) of the miniature and the scaled-up model are to be the same, how many inches in height will the scaled-up Pyramid? Give your answer to two places of decimal.

---

Assume the pyramid is solid. Then if the linear measurements are scaled by
a factor lambda, then the volume is scaled by lambda^3.

So let the scale factor be lambda.

For the masses to be the same if the large pyramid has a density 1/8
of the small, then the volume of the larger must be 8 times that of the
smaller. So lambda^3=8, and so lambda=2.

Hence the height of the scaled up pyramid will be 6 inches.

RonL

thanks I was just starting to think it would be 24inches because multiply by 8 so thanks