A cylinder with radius r=0.75 m and height h = 1 m has to be covered by a cone. Find the minimal area for the cone.
Surface Area of Cone: pi*r^2 + pi*r*L
So, I figured out:
H= Height of the cone
R= Radius of the cone
(H-1)/0.75 = H/R
H=-4R/(-4R+3)
To calculate L, I used the Pythagoras & substituted H from above:
L = sqrt(R^2+H^2)
L = sqrt(R^2+(-4R/(-4R+3))
L = (sqrt(16R^4-24R^3+25R^2)/(4R-3)
I see I'm heading towards something really complicated...
Could you please help me find the right way to do it? I have just started doing this.