Question

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.

Answer 1

have you tried anything yet?

Answer 2

\(\huge a. \) 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 = \(\huge \frac{24}{30} \)
in the simplest form, this reduces to \(\huge \frac{4}{5} \)

Answer 3

\(\huge b. \) we are quite fortunate that one of the volumes was given, so we can find the base areas and hence, find the ratio.

\(\huge \text{volume of pyramid= base area * height} \)
\(\huge \text{base area =}\frac{\text{volume of pyramid}}{height} \)
\(\huge \text{base area =}\frac{16000}{30}=533.33m^2\)
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

\[\huge \frac{V_2}{16000}=\frac{24}{30} \]
\(\huge V_2 =\frac{24*16000}{30}=12800m^3 \)

this means the base area for the smaller pyramid is:
\(\huge base \ area = \frac{volume(V_2)}{height}=\frac{12800}{24}=533.33m^2 \)
this means that the ratio of the base areas are:
533.33:533.33=\(\large \frac{533.33}{533.33}=1 \)

Answer 4

you should be able to do c and d on your own :)