Using implicit differentiation, it is found that the rate of change of the volume of the sphere at that instant is of 1815.84 cubic centimetres per minute.
The volume of a sphere of radius r is given by:
[tex]V = \frac{4\pi r^3}{3}[/tex]
Applying implicit differentiation, the rate of change is of:
[tex]\frac{dV}{dt} = 4\pi r^2\frac{dr}{dt}[/tex]
In this problem, we have that [tex]\frac{dr}{dt} = 0.5, r = 17[/tex], thus:
[tex]\frac{dV}{dt} = 4\pi (17)^2(0.5) = 1815.84[/tex]
The rate of change of the volume of the sphere at that instant is of 1815.84 cubic centimetres per minute.
A similar problem is given at https://brainly.com/question/11496075
