A cylinder is inscribed in a cone as shown in the figure. The radius of the cone is 4 inches and the height is 7 inches. Express the volume, V, of the cylinder in terms of its height, h.

I found the volume of the cylinder which is:
(4pi/27)(r^2h). But I am not sure how to replace the r^2 with h since the answer needs to be in terms of h. Any help is very thankfully appreciated!

Question

A cylinder is inscribed in a cone as shown in the figure. The radius of the cone is 4 inches and the height is 7 inches. Express the volume, V, of the cylinder in terms of its height, h.

I found the volume of the cylinder which is:
(4pi/27)(r^2h). But I am not sure how to replace the r^2 with h since the answer needs to be in terms of h. Any help is very thankfully appreciated!

anonymous · Answer

|dw:1347200090533:dw| r1 is the radius of cone and r2 is the radius of cylinder. h1 and h2 respectively!~
$$\frac{ (h1-h2) }{ r2 }=\frac{ h1 }{r1 }$$
and in this case $$\frac{ 7-h2 }{ r2 }=\frac{ 7 }{ 4 }$$
so it is easy for you to get the relationship between r2 and h2
and you can find the V of this cylinder~