Neco 2023 Mathematics Question 11

A solid consists of a right circular cylinder of radius \( r \) cm and height \( h \) cm. A hemisphere of the same radius is attached to the top of the cylinder. On one lateral side of the cylinder a right square pyramid whose base side length is \( 2r \) cm and whose height is \( \dfrac{h}{2} \) cm is attached, sharing its square base with a rectangular portion of the cylinder's lateral surface. The total surface area of the solid, excluding the base of the cylinder that rests on the floor, is \( 1500 \) cm\(^2\). If the height of the cylinder is three times its radius (\( h = 3r \)) and \( \pi = \dfrac{22}{7} \), find the radius \( r \) correct to two decimal places.