The axial section of the cylinder is a square with a diagonal of 8√2 cm. Find the volume of the cylinder.

To find the volume of a cylinder, you need to know its height and radius. If the square is the axial section of the cylinder, then the height of the cylinder is equal to the diameter of its base or two radii.
Find the side of a square using the Pythagorean theorem for a triangle formed by two adjacent sides and the diagonal, which is the hypotenuse.
a ^ 2 + a ^ 2 = (8√2) ^ 2,
2a ^ 2 = 128
a = 8cm = h (height) = 2r (base radius).
Let’s consider n – this is pi equal to 3.14.
V cylinder = (pi) r ^ 2 × h
V = 3.14 × 16 × 8 = 401.92 cm ^ 3 or just 128n cm ^ 3