A rectangular parallelepiped is inscribed in a cylinder, the axial section of which is a square with an area of 1 m2.

| March 24, 2021 | education

A rectangular parallelepiped is inscribed in a cylinder, the axial section of which is a square with an area of 1 m2. Find the sides of the base of the box at which its volume will be greatest.

Since the axial section of the cylinder is a square with an area of ​​1 m2, then AB = AD = BC = CD = 1 s.

At the base of the parallelepiped there is a rectangle, since the sum of the opposite angles of the quadrilateral inscribed in the circle is 180.

Then the length of the diagonal is РН = АD and is equal to the diameter of the circle at the base of the cylinder.

The area of ​​the rectangle at the base of the parallelepiped is:

Sbn = НР2 * SinROM / 2.

The maximum area will be at SinROM = 1.

Angle POM = 90, then there will be a square at the base of the parallelepiped.

2 * НМ ^ 2 = НР ^ 2 = 1.

HM ^ 2 = 1/2.

HM = √2 / 2 cm.

Answer: The maximum volume of a parallelepiped will be with a side equal to √2 / 2 cm.



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