A rectangular parallelepiped is inscribed in the cylinder, the diagonal of which is equal to m and makes an angle a with the base plane. Find the volume of the cylinder.
1) First, find the height of the cylinder.
h = m * sin a.
2) Then, we find the diameter of the cylinder.
d = m * cos a.
3) The area of the base of the cylinder is found by the formula.
S = pi * r ^ 2, where r is the radius of the base.
4) The radius of the circle is half the diameter of the circle.
r = 1/2 * d = d / r;
5) The volume of the cylinder is found by the formula V = S * h.
V = S * h = pi * r ^ 2 * m * sin a = pi * (d / 2) ^ 2 * m * sin a = pi * d ^ 2/2 * m * sin a = pi * m * cos a * m * cos a / 2 * m * sin a = 1/2 * pi * m ^ 3 * cos ^ 2 a * sin a.
Answer: V = 1/2 * pi * m ^ 3 * cos ^ 2 a * sin a.
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