Answer:
68.445 cm³/s
Explanation:
Given:
Volume, V = [tex]\frac{4}{3}\pi r^3[/tex]
radius = 5.85 cm
Growth rate of radius = 0.5 cm/week
now
differentiating the volume with respect to time 't', we get:
[tex]\frac{dV}{dt}=\frac{d(\frac{4}{3}\pi r^3)}{dt}[/tex]
or
[tex]\frac{dV}{dt}=(\frac{4}{3}\pi )3r^2\frac{dr}{dt}[/tex]
now, substituting the value of r (i.e at r = 5.85cm) in the above equation, we get:
[tex]\frac{dV}{dt}=4\pi 5.85^2\times 0.5[/tex]
or
[tex]\frac{dV}{dt}=68.445cm^3/s[/tex]
hence, the rate of change of volume at r = 5.85cm is 68.445 cm³/s
