Question

The ratio of the heights of two similar pyramids is 3:2. The volume of the larger pyramid is 135 cm3. What is the volume of the smaller pyramid?

Answer 1

`l-larger\\s-smaller\\\\(h_l)/(h_s)=(3)/(2)\to(V_l)/(V_s)=\left((3)/(2)\right)^3\\\\V_l=135\ cm^3.\\subtitute\\\\(135)/(V_s)=(27)/(8)\ \ \ \ |cross\ multiply\\\\27V_s=135\cdot8\\\\27V_s=1080\ \ \ |divide\ both\ sides\ by\ 27\\\\\boxed{V_s=40\ (cm^3)}`