Question

The height of one solid limestone square peer amid is 24 m. A similar solid limestone square peer med has a height of 30 m. The volume of the larger pier mid is 16,000 meters cubed. Determine each of the following, showing all your work and reasoning. A, the scale factor of the small pier mid to large apartment in simplest form

Answer 1

I think what you meant here is that the limestone is in a shape of a square pyramid. Knowing the shape, we must also know the formula for its volume:

V=s²h/3, where
s is the side of the square base
h is the vertical height of the pyramid

First, you find the area of the base s² from the known volume of the larger pyramid.

16,000 = s²(30)/3
s² = 1,600

Then, assuming both pyramids have equal areas of bases, we can use this value for the smaller pyramid. We can determine its volume to be
V = (1,600)(24)/3 = 12,800

Thus, the scale factor for the small pyramid to the big pyramid is 12,800/16,000 or 4/5.