2024 THREE(d)

Jamie is doing some baking and pouring
the flour to form a conical pile.

The height of the pile is always the same
as the diameter of the base of the cone.

If the flour is being added at a constant
rate of $3{\mathrm{cm}}^3$ per second, at what rate is
the height increasing when the pile is
$4\mathrm{cm}$ in height?

*You must use calculus and show any*
*derivatives that you need to find when*
*solving this problem.*

Note that volume of a cone $=\frac{1}{3}\pi r^{2}h$.