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

A solid sphere is dissolving in a chemical solution. The surface area of the sphere, $A$ , is decreasing at a constant rate.

Show that the rate of decrease of the radius, $r$ , of the sphere is inversely proportional to $r$ .

You may use the following formula for the surface area of a sphere:

4\pi r^2

[5]

A solid sphere is dissolving in a chemical solution. The surface area of the sphere, $A$ , is decreasing at a constant rate.

Show that the rate of decrease of the radius, $r$ , of the sphere is inversely proportional to $r$ .

You may use the following formula for the surface area of a sphere:

4\pi r^2

[5]

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