SOLUTION: a hollow high circular cone stands on a horizontal table. it is 100cm high with base radius 20cm . it is filled with water through the vertex up to a depht of 25cm.. calculate the
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Question 1044466: a hollow high circular cone stands on a horizontal table. it is 100cm high with base radius 20cm . it is filled with water through the vertex up to a depht of 25cm.. calculate the area of the circle formed by the water surface and calculate the volume of the water inside the cone
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Consider a vertical cross-section of your cone. The 20 cm radius of the base, the 100 cm height, and a generator of the cone form a right triangle. You do not know the radius of the circular surface of the water, but you do know that the distance from the top of the water to the vertex of the cone must be 75 cm (100 minus 25). So that 75 cm portion of the height of the cone, the unknown radius, and a portion of the generator of the cone form a right triangle that is similar to the 100 cm by 20 cm triangle described earlier. Hence, you can solve:
for 
to find the radius of the surface of the water from which the area of the surface of the water follows directly using:
The volume of the portion of the cone that contains water is equal to the total volume of the cone minus the volume of that part of the cone that does not contain water. Use:
with the appropriate selections for 
and 
to calculate the necessary conical volumes.
John
My calculator said it, I believe it, that settles it
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