Answer:
The radius is changing at a rate of 2 cm/s
Explanation:
Here, we want to get the rate at which the radius of the balloon is changing
Mathematically, the formula for the volume of a sphere is:
[tex]\begin{gathered} V\text{ = }\frac{4}{3}\times\pi\times r^3^{}^{} \\ \\ \frac{dv}{dr}\text{ = 4}\times\pi\times r^2 \end{gathered}[/tex]From the question:
[tex]\frac{dv}{dt}\text{ = 1231.5 }[/tex][tex]\frac{dr}{dt}\text{ = ?}[/tex][tex]\frac{dr}{dt}\text{ = }\frac{dv}{dt}\times\frac{dr}{dv}[/tex]dr/dv is the reciprocal of dv/dr
Thus, we have it that:
[tex]\begin{gathered} \frac{dr}{dt}\text{ = 1231.5 }\times\frac{1}{4\times3.142\times7^2} \\ \\ \frac{dr}{dt}\text{ = 2 }\frac{cm}{s} \end{gathered}[/tex]