Find the volume of a pyramid inscribed in a cube if the edge of the cube is 3.

Since there are no restrictions on the pyramid, we will assume that the pyramid is inscribed as follows: the base of the pyramid coincides with the base of the cube, and its height will be equal to the height of the cube h = 3. Then the area of the base of the pyramid will be equal to the area of the square, which is the lower face of the pyramid with side a = 3;
S = a • a = 3 • 3 = 9 (square units).
We find the volume of the pyramid by the formula:
V = S • h: 3 = 9 • 3: 3 = 9 (cubic units).
Answer: 9 cubic meters. units