A rectangular parallelepiped is inscribed in the cylinder, the diagonal of which is equal to m

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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