Question

I need help with this! or someone check my work! THanks!!!

A right circular cylinder is inside a right circular cone of altitude h and radius base x. A. Derive a formula for the radius r of the cylinder in terms of h and x

if its lateral area is equal to the lateral area of the small cone which surmounts the cylinder.

Answer 1

\[A1/A2 = 2 \pi r h / \pi r \sqrt{h^2+ x^2} \]

Answer 2

Assumptions:
radius of cylinder is r, radius of cone is x,
height of cone= height of cylinder
lateral area of cylinder = lateral area of cone

This gives us
2Pi*r*h = Pi * x sqrt( h^2 + x^2)

Solve for r
r = Pi * x sqrt( h^2 + x^2) / (2Pi*h)

r = x sqrt(h^2 +x^2) / (2h )

Answer 3

Thanks a lot , you really helped me :)
Sorry didnt give credit on the right time :)

Answer 4

no problem :)

Answer 5

:)