Forming differential equations and connected rates of changeEdexcel International A Level Maths: Mind map

Exam questions on Forming differential equations and connected rates of change

1. At time $t$ minutes a leaking tank holds $V$ m$^3$ of water. Water leaks out at a rate proportional to the volume $V$ of water remaining in the tank.
   Find the rate at which the volume is changing when $V=80$.2 marks
2. A spherical balloon is inflated so that its radius $r$ cm increases at a constant rate of $0.5$ cm s$^{-1}$. The volume of a sphere is $V=\frac43\pi r^3$ and its surface area is $S=4\pi r^2$.
   Find the rate at which the surface area is increasing when $r=6$.2 marks
3. Liquid is poured at a constant rate of $20$ cm$^3$ s$^{-1}$ into an inverted cone with its axis vertical. At time $t$ seconds the depth of liquid is $h$ cm and its volume is $V=\frac13\pi h^3$ cm$^3$.
   Find the rate at which the depth is increasing when $h=5$.3 marks