Question

if two pyramids are similar and the ratio between the lengths of their edges is 2;7 what is the ratio of their volumes? ...?

Answer 1

The answer is 8:343

Explanation:

Answer 2

The answer is 8:343.

We can use Galileo's square cube law to calculate the ratio between two similar pyramids. The law is used to describe the change of the area or the volume of the shape when their dimensions increase or decrease:

`(V_1)/(V_2) =( (l_1)/(l_2) )^(3) \\`

V₁ and V₂ - volumes of pyramids,
l₁ and l₂ - the edges of pyramids.


`(V_1)/(V_2) =( (l_1)/(l_2) )^(3) \\ (V_1)/(V_2) =( (2)/(7) )^(3) \\ (V_1)/(V_2) = (2^(3))/(7^(3)) \\ (V_1)/(V_2) = (8)/(343) \\`