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What the problems look like

A few statements from this skill. Answers, hints and worked solutions live in the practice session.

1. Warm-up

   A circular oil slick spreads on water so that its radius increases at a constant rate of $3$ cm/s. At the instant the radius is $9$ cm, find the rate of change of the slick's area, $\frac{dA}{dt}$, in cm²/s. Give the exact value in terms of $\pi$.

2. Warm-up

   A circular oil slick spreads on water so that its radius increases at a constant rate of $8$ cm/s. At the instant the radius is $13$ cm, find the rate of change of the slick's area, $\frac{dA}{dt}$, in cm²/s. Give the exact value in terms of $\pi$.

3. Warm-up

   A circular oil slick spreads on water so that its radius increases at a constant rate of $2$ cm/s. At the instant the radius is $20$ cm, find the rate of change of the slick's area, $\frac{dA}{dt}$, in cm²/s. Give the exact value in terms of $\pi$.

Problems shown under their original terms: Generated (template, solver-computed).