Mathematics 9709 · AS & A Level · Differentiation

Differentiation — practice question

A spherical weather balloon is being inflated by a pump. Its volume is rising at a constant rate of $600\,\text{cm}^3$ per second. At the start of pumping, the balloon was empty.
(a)[2]

Find the balloon's radius after $30$ seconds.

(b)[3]

Find the rate at which the radius is increasing after $30$ seconds.

Worked solution & mark scheme

This 5-mark question has a full step-by-step worked solution and mark scheme. One marking point: Apply $\frac{4}{3}\pi r^3=18000$

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