The diagonal of the square base of a regular pyramid is 6dm, the height of the pyramid is 15dm.

The diagonal of the square base of a regular pyramid is 6dm, the height of the pyramid is 15dm. Find the volume of this pyramid.

Let’s find the area of the base of the regular pyramid (the area of the square).

S = a²;

The diagonal of the square is known to be 6 in. First, we find the sides of the square according to the Pythagorean theorem (the sum of the squares of the legs is equal to the square of the hypotenuse):

a² + b² = c²;

a² + a² = 6²;

a² + a² = 36;

a² = 36/2;

a = 18;

a = √18 – side of the square.

S square = (√18) ² = 18 dm².

The volume of a regular pyramid is:

V = 1/3 * S base * H (height of the regular pyramid);

V = 1/3 * 18 * 15 = 6 * 15 = 90 dm³ – the volume of the pyramid.

Answer: 90 dm³