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Wedge is formed by a plane cutting into a right circular cylinder of radius of 2 at an angle measure 30. The plane intersects the base of the cylinder in a diameter of the circular base.

2007-05-02 01:38:28 · 1 answers · asked by Anonymous in Science & Mathematics Mathematics

1 answers

Suppose the cylinder base is on the XY plane, with its center at the origin. Then, supposing the Z axis orthogonal to the XY plane, the cylinder equation is

x^2 + y^2 = r^2 = 4

Supposing the XY plane contains the X axis and its slope is 30 degres, its equation is z = tan(30) y = sqrt(3)/3 y.

The tringle vertexes on the XY axis have coordinates (-2, 0 ,0) and (2, 0, 0). The triangle base is therefore b =4, the circle diameter. The 3rd vertex has its y coordinate at a point (0, 2, z*) for some z. According to our equations, z* = sqrt(3)/3 . 2 = 2sqrt(3)/3. So, the triangle height is h = sqrt(z*2 + 2^2) = sqrt(4/3 + 4) = sqrt(16/3) = 4sqrt(3)/3.

Finally, the triangular cross section is S = b h/2 = (4 . 4sqrt(3)/2) = 8sqrt(3)/3

2007-05-02 02:51:34 · answer #1 · answered by Steiner 7 · 0 0

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