(a)[3]
Show that the tank's volume, $V\text{ cm}^3$, can be written as $V = \frac{\pi r(600-r^2)}{2}$.
(b)[3]
Find the exact value of $r$ corresponding to the maximum value of $V$.
(c)[2]
Hence, find the maximum value of $V$.
Mathematics 9709 · AS & A Level · Differentiation
Differentiation — practice question
A manufacturer plans to create an open cylindrical tank, as illustrated. The tank has a base but no lid. The tank's external surface area is fixed at $600\pi\text{ cm}^2$. Its radius $r$ cm and height $h$ cm may change.
Worked solution & mark scheme
This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Starting with $2\pi rh+\pi r^2=600\pi$, rearrange it to isolate $h$.” …
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