Question

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.
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

The question seems kinda murky. If you mean
dr/dt = kT
v = 4/3 πr^3
dv/dt = 4πr^2 dr/rt = 4π(kTt)^3

Answer 2

what is the "k" referring to?

Answer 3

"y is directly proportional to x" means that
y = kx
for some constant k.
C'mon, man, that is Algebra I