# a cylinder is inscribed in a cone

• Mar 16th 2009, 08:55 PM
katinthehat108
a cylinder is inscribed in a cone
A cylinder is inscribed in a cone. The cylinder has an altitude of 15 cm and a radius of 3 cm. Express H as a function of R.

Thanks!
• Mar 16th 2009, 11:23 PM
Soroban
Hello, katinthehat108!

I think I know what you meant . . .

Quote:

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: . $\frac{H-15}{3} \:=\:\frac{15}{R-3} \quad\Rightarrow\quad (H-15)(R-3) \:=\:45$

. . . . $HR - 3H - 15R + 45 \:=\:45 \quad\Rightarrow\quad HR - 3H \:=\:15R$

. . . . $H(R-3) \:=\:15R \quad\Rightarrow\quad\boxed{ H \:=\:\frac{15R}{R-3}}$