1.7.18 Chain rule (A-level only)

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

Show that the rate of decrease of the radius, $r$ , of the balloon is inversely proportional to $r^2$ .

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

\frac{4}{3}\pi r^3

[4]

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

Show that the rate of decrease of the radius, $r$ , of the balloon is inversely proportional to $r^2$ .

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

\frac{4}{3}\pi r^3

[4]

1.7.18 Chain rule (A-level only) Questions