The height of one square pyramid is 12 m. A similar pyramid has a height of 6 m. The volume of the larger pyramid is 400 m3. Determine each of the following, showing all your work and reasoning: (a) Scale factor of the smaller pyramid to the larger pyramid in simplest form (b) Ratio of the areas of the bases of the smaller pyramid to the larger pyramid (c) Ratio of the volume of the smaller pyramid to the larger (d) Volume of the smaller pyramid

Question

Mathematics

Zaiden Charles

3 September, 02:00

The height of one square pyramid is 12 m. A similar pyramid has a height of 6 m. The volume of the larger pyramid is 400 m3. Determine each of the following, showing all your work and reasoning: (a) Scale factor of the smaller pyramid to the larger pyramid in simplest form (b) Ratio of the areas of the bases of the smaller pyramid to the larger pyramid (c) Ratio of the volume of the smaller pyramid to the larger (d) Volume of the smaller pyramid

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Bella Hopkins · Answer 1

A) Scale factor of the smaller pyramid to the larger pyramid in simplest form:

6 m / 12 m = 1/2

b) Ratio of the areas of the bases of the smaller pyramid to the larger pyramid:

(1/2) ^2 = 1/4

c) Ratio of the volume of the smaller pyramid to the larger:

(1/2) ^3 = 1/8

d) Volume of the smaller pyramid:

(1/8) * 400 m^3 = 50 m^3