The height of one solid limestone square pyramid is 25 m. A similar solid limestone square pyramid has a height of 30 m. The volume of the larger pyramid is 16,200 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

Answers:

(A) Scale factor = 5/6 or 0.833

(B) Area ratio is 25:36

(C) Volume ratio is 125:216

(D) Volume of smaller pyramid = 9375m^3

Explanation:

A) The formula for the scale factor for pyramids is:

Scale factor = Height of small pyramid/Height of large pyramid

Scale factor = 25/30

Scale factor = 5/6 or 0.833

B) The ratio of the area of the base of the smaller pyramid to the larger pyramid = (25) ^2 / (30) ^2

Hence area ratio is 25:36

C) Ratio of the volume of the smaller pyramid to the larger = (25) ^3 / (30) ^3

Therefore volume ratio is 125:216

D) Volume of smaller pyramid is 125/216 times the volume of the larger pyramid, from above,

Therefore volume of smaller pyramid = 125/216 * 16200 = 9375m^3