Question

What is the similarity ratio of the smaller to the larger similar pyramids? Enter your answer as a:b.

Answer 1

Similarity ratio is the ratio of two corresponding sides. The ratio of volumes is 343:1331 which is the ratio of the sides cubed. Similarity ratio = cube root of 343: cube root of 1331 = 7:11

Answer 2

→Volume is proportional to cube of side length.

So, Ratio of volume of two pyramids is equal to ratio of the cubes of their Side Length.

If first pyramid has side length =a units

And Second pyramid has side length = b units

`(V_(1))/(V_(2))=(a^3)/(b^3)`

`(343)/(1331)=[(a)/(b)]^3\\\\ ((7)/(11))^3=[(a)/(b)]^3\\\\ (a)/(b)=(7)/(11)`

a:b=7:11