In a regular quadrangular pyramid, the side of the base = 8cm, and the side rib is inclined to the plane

| September 1, 2021 | education

In a regular quadrangular pyramid, the side of the base = 8cm, and the side rib is inclined to the plane of the base at an angle of 45 degrees. Find the volume of the pyramid.

Determine the length of the AC diagonal at the base of the pyramid.

Since there is a square at the base of the pyramid, its diagonal is: AC = AB * √2 = 8 * √2 cm.

Point O divides the diagonals of the square in half, then OS = AC / 2 = 8 * √2 / 2 = 4 * √2 cm.

Determine the length of the height of the pyramid, from the right-angled triangle POC. Since in a right-angled triangle one of the angles is 450, the legs of this triangle are equal.

RO = OS = 4 * √2 cm.

Determine the area of the base of the pyramid.

Sbn = AB ^ 2 = 64 cm2.

Then V = Sosn * PO / 3 = 64 * 4 * √2 / 3 = 256 * √2 / 3 cm3.

Answer: The volume of the pyramid is 256 * √2 / 3 cm3.



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