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

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