Answer:
[tex]undefined[/tex]
Explanations:
The formula for calculating the volume of spheres is expressed as:
[tex]V=\frac{4}{3}\pi r^3[/tex]
The rate of change of volume of the sphere is given as:
[tex]\begin{gathered} \frac{dV}{dt}=\frac{dV}{dr}\cdot\frac{dr}{dt} \\ \frac{dV}{dt}=4\pi r^2\cdot\frac{dr}{dt} \end{gathered}[/tex]
a) Given the following parameters:
[tex]\begin{gathered} \text{radius }r\text{ =}8inches \\ \frac{dr}{dt}=5in\text{/min} \end{gathered}[/tex]
Substitute into the result to have:
[tex]\begin{gathered} \frac{dV}{dt}=4\pi(8)^2\cdot5 \\ \frac{dV}{dt}=4\pi\times64\times5 \\ \frac{dV}{dt}=1280\pi in^3\text{/min} \end{gathered}[/tex]
b) If the radius is 37inches, the rate of change of the volume is given as:
[tex]\begin{gathered} \frac{dV}{dt}=4\pi(37)^2\cdot5 \\ \frac{dV}{dt}=4\pi\times1369\times5 \\ \frac{dV}{dt}=27,380\pi in^3\text{/min} \end{gathered}[/tex]
