2026 RI Promo Q1

[It is given that a sphere of radius \(r\) units has surface area \(4\pi r^2\).]

The diagram shows a sphere inscribed in a cylinder with base radius \(r\) units. The sphere remains inscribed within the cylinder as the volume of the cylinder increases at a rate of \(2\text{ units}^3\) per minute. Find the exact rate of change of the surface area of the sphere when the volume of the cylinder is \(16\pi\text{ units}^3\).[4]