Question

The height of one solid limestone square pyramid is 12 m. A similar solid limestone square pyramid has a height of 15 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

a) The scale factor of the small pyramid to the large pyramid is 4/5

b) The ratio of area of the base of the smaller pyramid to

the larger pyramid is 16/25

c) The ratio of the volume of the smaller pyramid to the volume

of the larger pyramid is 64/125

d) The volume of the smaller = 8192 m³

Explanation:

∵ The height of the small pyramid is 12 m

∵ The height of the large pyramid is 15 m

∵ The two pyramid are similar

∴ The ratio between their heights = 12/15 = 4/5

a) The scale factor of the small pyramid to the large pyramid is:

4/5

∵ The two pyramid are similar with scale factor 4/5

∴ The area of the small base/ the area of the larger base = (4/5)²

b) The ratio of area of the base of the smaller pyramid to

the larger pyramid is 16/25

∵ The two pyramid are similar with scale factor 4/5

∴ The volume of the small/ the volume of the larger = (4/5)³

c) The ratio of the volume of the smaller pyramid to the volume

of the larger pyramid is 64/125

d) ∵ The volume of the larger pyramid = 16000 m³

∴ The volume of the smaller = (16000 × 64) ÷ 125 = 8192 m³