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 2006-11-12 15:30:15