Code:
|\                  \
| \
|  \
|___\               sector side = cone side
| 5  \     \
|     \    cut cone side
|H     \
|__10___\  /        /
- A cone side surface is a Sector
- A cut cone side surface is a sector with removed inner sector.
- The sector side is the extrapolated cone side; the crossection of the
cone can be divided into 2 perpendicular triangles, with
same angles => equilateral, and ratio is 1:2 (the figure)
=> The sector side is 2 times cut cone side
=> the sector Area/cone side surface Area is 3/4 since,
<= (the ratio was 2 => the inner sector/outher sector=
1^2*pi*radius^2/2^2*pi*radius^2=1/4)
- the area of a sector is theta*radius^2/2 (theta=sector angle)
- theta = arc/radius (by definition)
=> Sector area= arc*radius/2
- the arc of the sector is the circumference of the bottom circle which is 
2*10*pi=20pi
- the radius is 2 times the cone side, 2*sqr(5^2+H^2) (pythagoras)
=> The Cone side is now:
3/4 * 20pi * sqr(25+H^2) = (320-5^2-10^2)pi = 195pi (bottom and top surfaces removed)
=> sqr(25+H^2)=13
=> H=12