Two planes cut a right circular cylinder to form a wedge. One plane is perpendic

Question

Two planes cut a right circular cylinder to form a wedge. One plane is perpendicular to the axis of the cylinder and the second makes an angle of theta degrees with the first (see figure). (Use r for the radius.) (a)Find the volume of the wedge if theta = 45 degree. If we let z be the height of the wedge, from the geometry we get at a pact; (x, y): tan(theta) = z/x where: z = xtan(theta) At 45 degrees of theta: tan(45 degrees) = 1 = = > x = z Based on the above information, the wedge face consist of isosceles right triangles. What is the equal length and base? Give thickness of the wedge: Give the face area is terms of x and then in terms of y: Give the differential volume in terms of y: Integrate, and then give the volume;

Explanation / Answer

Volume =2/3 r^3

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