In a regular quadrangular pyramid SABCD with base ABCD, the side edge is SC -37

| March 19, 2021 | education

In a regular quadrangular pyramid SABCD with base ABCD, the side edge is SC -37, and the side of the base is 35√2, find the volume of the pyramid.

Since there is a square at the base of the regular pyramid, the triangle ACD is rectangular and isosceles, then, according to the Pythagorean theorem, the length of the hypotenuse AC will be equal to:

AC ^ 2 = 2 * CD ^ 2 = 2 * (32 * √2) ^ 2 = 4900.

AC = 70 cm.

The diagonals of the square at point O are divided in half, then OS = AC / 2 = 70/2 = 35 cm.

In a right-angled triangle SОС, we determine the length of the leg SO.

SO ^ 2 = SC ^ 2 – OC ^ 2 = 1369 – 1225 = 144.

SO = √144 = 12 cm.

The area of the base of the pyramid is equal to: Sbn = СD ^ 2 = 2450 cm2.

Then Vpir = Sbn * SO / 3 = 2450 * 12/3 = 9800 cm3.

Answer: The volume of the pyramid is 9800 cm3.



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