SOLUTION: 2 planes intersect a cylinder of radius r.
The line generated is a diameter of the cylinder.
1 plane is normal to the axis of the cylinder.
The angle between the planes is B.
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-> SOLUTION: 2 planes intersect a cylinder of radius r.
The line generated is a diameter of the cylinder.
1 plane is normal to the axis of the cylinder.
The angle between the planes is B.
-
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Question 1158670: 2 planes intersect a cylinder of radius r.
The line generated is a diameter of the cylinder.
1 plane is normal to the axis of the cylinder.
The angle between the planes is B.
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Find the volume of the "wedge" generated. Answer by Alan3354(69443) (Show Source):
You can put this solution on YOUR website! -------------------------
2 planes intersect a cylinder of radius r.
The line generated is a diameter of the cylinder.
1 plane is normal to the axis of the cylinder.
The angle between the planes is B.
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Find the volume of the "wedge" generated.
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Interesting problem, for a change.
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The volume dV of the slice from y to y+dy = A(y)*dy where A(y) is the area of the triangle that forms one face of the slice.
A(y) = x*h/2
h = x*tan(B)
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x^2 + y^2 = r^2
--> x^2 = r^2 - y^2
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A(y) = x^2*tan(B)/2 = tan(B)*(r^2 - y^2)/2
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Volume = INT[tan(B)*(r^2 - y^2)/2 dy] from -r to r
tan(B)/2 is a constant.
---> cubic units
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I can send some sketches if you want.
