A cuboid PQRS TUVW has dimensions PQ=3cm, QR=4cm, and the distance from the center of the base to vertex P is 2.5cm. Find the length of QR and the angle between the diagonal PR and the side PQ.

The problem describes a cuboid with given dimensions and asks for projections and angles.
From the figure and given values:
PQ = 3 cm.
PO = 2.5 cm. Assuming O is the center of the base PQRS, then PR (diagonal of the base) = $2 \times PO = 2 \times 2.5 = 5$ cm.
In the right-angled triangle PQR, $QR = \sqrt{PR^2 - PQ^2} = \sqrt{5^2 - 3^2} = \sqrt{25 - 9} = \sqrt{16} = 4$ cm.