(a)[3]
Determine the rate of increase of the mound's radius at the moment when the radius is $5.5\ \text{m}$.
(b)[3]
Find the volume of the mound at the instant when the radius is increasing at $0.1\ \text{m}$ per second.
Mathematics 9709 · AS & A Level · Differentiation
Differentiation — practice question
The volume $V\ \text{m}^3$ of a large circular mound of iron ore with radius $r\ \text{m}$ is represented by $V = \frac{3}{2}\left(r - \frac{1}{2}\right)^3 - 1$ for $r \geq 2$. Iron ore is being added to the mound at a steady rate of $1.5\ \text{m}^3$ per second.
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This 6-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Differentiate to get $\dfrac{dV}{dr}=\dfrac92\left(r-\tfrac12\right)^2$.” …
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