Suppose the pyramid in the above diagram has a square base with side length \(8\text{ cm}.\) If the volume of the pyramid is \(320\text{ cm}^3,\) what is its height in \(\text{cm}?\)

If \(x=6,\) \(y=10\) and \(z=\sqrt{136},\) what is the volume of the rigid body which can be formed by the above planar figure?

Note: The above diagram is not drawn to scale.

If a regular octahedron is inscribed in a sphere with radius \(r=8,\) as shown above, what is the volume of this regular octahedron?

What is the volume of the above tetrahedron with six identical edges of length \(5 ?\)

If \(x=6,\) \(y=16,\) and \(z=11,\) what is the volume of the water contained in the box, given that the water just touches the corner at \( B\). Give your answer in \(\text{cm}^3 ?\)