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1.9.15 Rates of change with the chain rule (A-level only)

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Question 15

A spherical weather balloon is leaking helium. The volume, VVV, of the balloon is decreasing at a constant rate.

Show that the rate of decrease of the radius, rrr, of the balloon is inversely proportional to r2r^2r2.

You may use the following formula for the volume of a sphere:

V=43πr3 V = \frac{4}{3}\pi r^3 V=34​πr3
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1.9.15 Rates of change with the chain rule (A-level only) Questions

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