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

not sure if you're still there, and assuming the cyl is inscribed in the cone like in my sketch then:|dw:1346822307326:dw|
Area of the large triangle = 1/2*28 = 1/2*(7-h)*r + 1/2*(4-r)*h + r*h
that gives you a second equation with r and h...

anonymous · Answer

Hi, Rhope.
We know that the Vcylinder = 4/9 Vcone
and Vcylinder = (pi)(r^2)(h)  and Vcone = 1/3(B)(H) 
where: B= area of lower surface of cone and H=the height of cone.
|dw:1346826272422:dw|