Step-by-step explanation:
We have equation for volume of a sphere
[tex]V=\frac{4}{3}\pi r^3[/tex]
where r is the radius
Differentiating with respect to time,
[tex]\frac{dV}{dt}=\frac{d}{dt}\left (\frac{4}{3}\pi r^3 \right )\\\\\frac{dV}{dt}=\frac{4}{3}\pi \times 3r^2\times \frac{dr}{dt}\\\\\frac{dV}{dt}=4\pi r^2\times \frac{dr}{dt}[/tex]
Given that
Radius, r = 24 cm
[tex]\frac{dr}{dt}=0.3cm/s[/tex]
Substituting
[tex]\frac{dV}{dt}=4\pi r^2\times \frac{dr}{dt}\\\\\frac{dV}{dt}=4\pi \times 24^2\times 0.3\\\\\frac{dV}{dt}=2171.47cm^3/min[/tex]
At the moment when the radius is 24 centimeters, the volume is increasing at a rate of 2171.47 cm³/min.
