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Nets, Sectors and Cones (Posted on 2006-11-12) Difficulty: 2 of 5
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.

No Solution Yet Submitted by Ansh    
Rating: 4.3333 (3 votes)

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Solution Solution Comment 2 of 2 |
 
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
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