Just in case a picture helps...

Related rates nearly always depend on the chain rule, so you might want to try filling up this pattern...

... where straight continuous lines differentiate downwards (integrate up) with respect to the main variable (in this case time), and the straight dashed line similarly but with respect to the dashed balloon expression (the inner function of the composite which is subject to the chain rule).

So what have we got here? V, dV/dt, a choice of either r or h because they depend on each other, and then you're trying to find dr/dt. Writing h as 2r for part (a), the Volume formula for a cone becomes the top row here...

So differentiate with respect to r...

Now just replace dV/dt with 2/5 and r with 4 in the bottom row, to determine the corresponding value of dr/dt.

For part (b), get the Volume formula in terms of h, and do similarly...

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Don't integrate - balloontegrate!

Balloon Calculus: Gallery

Balloon Calculus Drawing with LaTeX and Asymptote!