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I've got this problem: I have a cone (cone $A$) with a radius $8$ and a height of $12$. Now lets say that cone $A$ has a thickness of $2$. This thickness can be found from the bottom and inward and from the sides inward as well. I need to find the volume of the shell that is remaining. I do not yet know the height of the middle cone, only its radius. I've attached a look-alike picture to help give an idea. Any help is appreciated!

Imagine it like this, but with the cone in the middle being the thickness ($2$) inwards (up inside the other cone):

enter image description here

mrtaurho
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TheCreatorzOne
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  • you can find out those dimensions by similar triangles. the radius of the smaller cone is 2. use similar triangles to find the height. – user29418 Oct 30 '18 at 19:37
  • You do not need to know the height of the inner cone to find its volume. It is similar, which means that all corresponding measurements (e.g. radius and height) will have the same proportionality. – Doug M Oct 30 '18 at 20:10
  • I assume the radius of the inner cone, which you know, is about $4.26$? – Jens Oct 30 '18 at 20:36

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