LPQ is the sector of a circle of radius x cm centered at L, where PQ is the arc portion of its boundary. Angle PLQ is 120 degrees.
The sector is turned into a cone, with PQ forming the circular base. The curved surface area of the cone is A cm^2, and its volume is V cm^3. The height of the cone is h cm. Given that V = 3 A, find h.
Let r be the radius of the base of the cone.
Then,
V = (1/3)(pi)(r^2)(h)
A = (pi)(r)(x)
(2)(pi)(r) = (2/3)(pi)(x)
V = 3A
Solving for h gives
h = 27 cm

Posted by Bractals
on 20061112 15:30:15 