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

| September 14, 2021 | education

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.



One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.