what is the area of the largest rectangle formed when a plane intersects a right circular cylinder with a diameter of 12cm and a height of 15cm?
That would occur when the plane cuts the cylinder from above, parallel to and through the axis of symmetry. If the plane does not cut through parallel to the axis, or enters a curved side of the cylinder, you don't get a rectangle for the intersection area.
The answer is therefore 12 x 15 = 180 cm^2.