Hello, katinthehat108!
I think I know what you meant . . .
A cylinder is inscribed in a cone.
The cylinder has an altitude of 15 cm and a radius of 3 cm.
Express H (height of the cone) as a function of R (radius of the cone). Code:
- * -
: /|\ :
: / |:\ H-15
: / |::\ :
: *---+---* -
H /| | 3 |\ :
: / | | |:\ 15
: / | | 15|::\ :
: / | | |:::\ :
: / | | |::::\ :
- *-----*---+---*-----* -
: 3 : R-3 :
: -- R -- :
The two shaded triangles are similar.
Hence, we have: .$\displaystyle \frac{H-15}{3} \:=\:\frac{15}{R-3} \quad\Rightarrow\quad (H-15)(R-3) \:=\:45$
. . . . $\displaystyle HR - 3H - 15R + 45 \:=\:45 \quad\Rightarrow\quad HR - 3H \:=\:15R $
. . . . $\displaystyle H(R-3) \:=\:15R \quad\Rightarrow\quad\boxed{ H \:=\:\frac{15R}{R-3}}$