In the production process of a glass sphere, hot glass is blown such that the radius, r cm, increases over time (t seconds) in direct proportion to the temperature (T °C) of the glass.

Question

Find an expression, in terms of r and T, for the rate of change of the volume (V cm^3) of a glass sphere.

Answer 1

dr/dt = (k T)

v= (4/3) pi r^3
dv/dt = (4 pi) r^2 dr/dt ( in other words proportional to surface area of sphere)
dv/dt = (4 pi) r^2 dr/dt = (4 pi k T ) r^2