2025 SMBSS P1 Q4

The volume, \(V\text{ m}^3\), of water in a river may be modelled by the equation \(V=\dfrac23\pi x^3\), where \(x\) m is the depth of the water in the river. During a period of rainfall, the volume of water in the river increases at a rate of \(0.5\text{ m}^3/\text{h}\).

Find the rate at which the depth of the water in the river is increasing when \(x=0.8\).[4]