Answer:
The radius is growing with the rate of 0.07 cm per sec
Explanation:
Given,
The volume of the balloon ( spherical ),
[tex]V=\frac{4}{3}\pi r^3[/tex]
Where,
r = radius of the balloon,
Differentiating with respect to t ( time ),
[tex]\frac{dV}{dt}=\frac{4}{3}\times 3\pi r^2 \frac{dr}{dt}[/tex]
[tex]\frac{dV}{dt}=4\pi r^2\frac{dr}{dt}[/tex]
Here, [tex]\frac{dV}{dt}=15\text{ cubic cm per sec}[/tex] and r = 4 cm,
[tex]15=4\pi (4)^2 \frac{dr}{dt}[/tex]
[tex]\implies \frac{dr}{dt}=\frac{15}{64\pi}=0.0746\approx 0.07\text{ cm per sec}[/tex]
