Inscribed a right circular cylinder of height h and radius r in a cone of fixed radius R and fixed height H. Express the volume V of the cylinder as a function of r.
Inscribed a right circular cylinder of height h and radius r in a cone of fixed radius R and fixed height H. Express the volume V of the cylinder as a function of r. ...
Hello,
I've attached a diagram (see attachment)
You have 2 similar right triangles:
- the big one with the legs H and R
- the small on with the legs (H-h) and r.
Set up the proportion:
. Solve for r:
Plug in this term into the formula of the volume of a cylinder: