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."

I don't necessarily want an answer, just an explanation. Thank you!

Answer 1

so take the heights and use that as the scaling factor

linear scaling factors

smallest : largest
24 : 30 or 24/30

simplify this

for B you need to know for similar areas, square each term in the ratio

so use the simplified linear ratio and square both terms

C for Volume you cube the linear ratio

so use the simplified linear ratio from A and cube each term.

so to find the volume of the smaller pyramid




\[\frac{little^3}{larger^3} = \frac{x}{16000}\]

just solve for x

Answer 2

@campbell_st I understand section A. If it's not too much of a hassle, could you elaborate on B - D? I just need examples of the equations I'd use to solve the problems, replacing the actual numbers with defined variables.