Answer:
Volume increasing rate = [tex]62831.85 mm^3/s[/tex]
Explanation:
We rate of change of radius of sphere, [tex]\frac{dr}{dt} =2mm/s[/tex]
Diameter of sphere = 100 mm
Radius of sphere = 50 mm
Volume of sphere, V = [tex]\frac{4}{3} \pi r^3[/tex]
Rate of change of volume = [tex]\frac{dV}{dt}[/tex]
[tex]\frac{dV}{dt}=\frac{d}{dt} (\frac{4}{3} \pi r^3)=\frac{4}{3} \pi\frac{d}{dt}(r^3)=\frac{4}{3} \pi*3r^2*\frac{dr}{dt}[/tex]
Substituting known values
[tex]\frac{dV}{dt}= \frac{4}{3}* \pi*3*50^2*2=62831.85 mm^3/s[/tex]
Volume increasing rate = [tex]62831.85 mm^3/s[/tex]
