SOLUTION: A conical vessel has a height of 24 cm. and a base diameter of 12 cm. It holds water to a depth of 18 cm. above its vertex. Find the volume of its content in cc.

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Question 1210437: A conical vessel has a height of 24 cm. and a base diameter of 12 cm. It holds water to a depth of 18 cm. above its vertex. Find the volume
of its content in cc.
Answer by ikleyn(52990) About Me  (Show Source):
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A conical vessel has a height of 24 cm. and a base diameter of 12 cm.
It holds water to a depth of 18 cm. above its vertex. Find the volume
of its content in cc.
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Write a proportion  "height to the base radius " equals "depth to the radius of water surface"

    24%2F6 = 18%2Fr


using the similarity of triangles.  From this proportion

    r = %286%2A18%29%2F24 = 18%2F4 = 4.5 centimeters.


To find the water volume, use the formula to the volume of a cone

    V = pi%2Ar%5E2%2Ah = 3.14159265%2A4.5%5E2%2A18 = 1145.110521 cm^3.


Round it reasonably  V = 1145.11 cm^3.    <<<---===  ANSWER

Solved.