Using implicit differentiation, it is found that the volume is expanding at a rate of 17 cubic inches per second.
The volume of an sphere of radius r is given by:
[tex]V = \frac{4\pi r^3}{3}[/tex]
Applying implicit differentiation, the rate of change in the volume is given as follows:
[tex]\frac{dV}{dt} = 4\pi r^2\frac{dr}{dt}[/tex]
In this problem, we have that the parameters are given as follows:
[tex]r = 2.6, \frac{dr}{dt} = 0.2[/tex]
Considering that the measures are given in inches and the time is in seconds, the rate of change of the volume, in cubic inches per second, is given by:
[tex]\frac{dV}{dt} = 4\pi r^2\frac{dr}{dt}[/tex]
[tex]\frac{dV}{dt} = 4\pi \times 2.6^2 \times 0.2 = 17[/tex]
More can be learned about implicit differentiation at https://brainly.com/question/25608353
#SPJ1
