SOLUTION: A cylinder is drawn in a cone of height, H, and base, R. If the height and radius of the cone are unknown, express the volume (V) of the cylinder as a function of the radius (r) of

Algebra ->  Expressions-with-variables -> SOLUTION: A cylinder is drawn in a cone of height, H, and base, R. If the height and radius of the cone are unknown, express the volume (V) of the cylinder as a function of the radius (r) of      Log On


   



Question 1065224: A cylinder is drawn in a cone of height, H, and base, R. If the height and radius of the cone are unknown, express the volume (V) of the cylinder as a function of the radius (r) of its base.
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
A drawing would help.

r, radius of the cylinder
h, height of the cylinder

Similar triangles can be identified from a drawing.
%28R-r%29%2Fh=R%2FH

h=%28R-r%29%28H%2FR%29

V, volume for the cylinder,
V=h%2Api%2Ar%5E2
V=%28R-r%29%28H%2FR%29%2Api%2Ar%5E2