Two similar pyramids have volumes in a ratio of \( 27: 64 \). What is the ratio of their heights? (meaning the original scale factor) Please type your answer in the form of a ratio ( \( x: y \) ) with no spaces.

1. For similar pyramids, the ratio of their volumes is equal to the cube of the ratio of their corresponding linear dimensions (such as heights). That is, if the height ratio is \( k \), then the volume ratio is \( k^3 \). 2. We are given the volume ratio: \[ k^3 = \frac{27}{64} \] 3. Taking the cube root of both sides, we have: \[ k = \sqrt[3]{\frac{27}{64}} = \frac{\sqrt[3]{27}}{\sqrt[3]{64}} = \frac{3}{4} \] 4. Therefore, the ratio of their heights is: \[ 3:4 \]