Alright so I have a cone with radius 59.75 and height 60.75. Given this I can find the volume of the cone. Now I need to find the volume of a cone that is essentially the same but with a height of 58.73. How do I find the radius of this smaller cone? I thought about using proportions, but that does not seem accurate at all.
[Math] find the volume of a cone within a cone
geometryvolume
Best Answer
It seems the following. If I rightly understood your picture, the smaller cone $S$ is similar to the bigger $B$. Since the volumes of the similar figures are proportional to the cubes of their linear sizes, we have
$$V_S=V_B\left(\frac {h_S}{h_B}\right)^3=\frac{\pi r_B^2 h_B}{3}\left(\frac {h_S}{h_B}\right)^3.$$