2. The height of one solid limestone square pyramid is 24 m. A similar solid limestone square pyramid has a height of 30 m. The volume of the larger pyramid is 16,000 m3. Determine each of the following, showing all your work and reasoning ... a) The scale factor of the smaller pyramid to the larger pyramid in simplest form ... b) The ratio of the area of the base of the smaller pyramid to the larger pyramid ... c) Ratio of the volume of the smaller pyramid to the larger ... d) The volume of the smaller pyramid ...

a. a scale factor is basically a number that tells how bigger or smaller an object is, relative to another. we have been given the heights of the 2 pyramids so we can work from there ... the easiest way is to find the ratio of the given heights, hence ratio of small pyramid to larger pyramid = 24:30 = 2430 in the simplest form, this reduces to 45

b. we are quite fortunate that one of the volumes was given, so we can find the base areas and hence, find the ratio. volume of pyramid = base area * height base area = volume of pyramid height base area = 1600030 = 533.33 m2 to find the base area of the smaller pyramid, we have to find it's volume. we can apply similarities to figure that out. here's how V2 16000 = 2430 V2 = 24∗16000 30 = 12800 m3 this means the base area for the smaller pyramid is: base area = volume (V2) height = 1280024 = 533.33 m2 this means that the ratio of the base areas are: 533.33:533.33 = 533.33533.33 = 1