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Difficulty guide

The label describes the problem, not your ability.

1/5 - Foundational

Warm-up setup; checks one basic idea.

2/5 - Routine exam skill

Normal syllabus skill; usually one main rule or interpretation.

3/5 - Standard multi-step

Exam-style problem with multiple steps or a common trap.

4/5 - Hard exam skill

High-end exam problem; combines methods carefully.

5/5 - Challenge

Stretch problem beyond normal exam pressure.

Question

A spherical balloon is being inflated. Its radius is rr cm and volume is V=43πr3.V=\frac43\pi r^3.
Total: 6 points

(a) Differentiate the volume formula with respect to time. (2 points)

(b) If dVdt=48π\frac{dV}{dt}=48\pi cm³/s, write an expression for drdt\frac{dr}{dt} in terms of rr. (2 points)

(c) Use your expression to find drdt\frac{dr}{dt} when r=4r=4 cm. (2 points)

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