Science:Math Exam Resources/Courses/MATH110/December 2015/Question 08 (b)/Statement

If a spherical tank of radius 2 metres is filled up to h metres with water, then the volume of water $V$ in the tank is given by the following function:

$V(h)=\pi h^{2}\left(2-{\frac {h}{3}}\right),$

where $h$ is measured from the deepest point in the tank.

(b) As the water is poured into the tank, at what rate is the volume of water in the tank changing with respect to the height of the water when the water is 1 m deep? What are the units of this quantity?