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

A spherical snowball is melting in the sun. The volume, $V$ , of the snowball is decreasing at a constant rate.

Show that the rate of decrease of the snowball's surface area, $A$ , is inversely proportional to its radius, $r$ .

You may use the following formulae for a sphere:

\frac{4}{3}\pi r^3 \quad \text{and} \quad A = 4\pi r^2

[5]

A spherical snowball is melting in the sun. The volume, $V$ , of the snowball is decreasing at a constant rate.

Show that the rate of decrease of the snowball's surface area, $A$ , is inversely proportional to its radius, $r$ .

You may use the following formulae for a sphere:

\frac{4}{3}\pi r^3 \quad \text{and} \quad A = 4\pi r^2

[5]

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