Answer:
According to the passage, we have the next equation:
![(dV)/(dt) = (4)/(3)\pi*3*r^(2)*(dr)/(dt) = K*(4\pi*r^(2) )](https://img.qammunity.org/2020/formulas/mathematics/high-school/sun587lb55egzxqix5rqxkloxwetn5gm0w.png)
where "K" is a proportional constant
Leaving at the end with the next equation:
![(dr)/(dt) = K](https://img.qammunity.org/2020/formulas/mathematics/high-school/as5law6ddnqntezp9yvo7lnt0lgla73myh.png)
Integrating the equation, we have:
![r=K*t+C](https://img.qammunity.org/2020/formulas/mathematics/high-school/41boboupk2s4sla47sfjtz2k4a36jwqxhx.png)
where "C" is a constant
Then, we have the 2 conditions for the problem:
1) t=0 → r=10
Replacing in the equation, we have C = 10
2) t=5 → r=8
Replacing in the equation, we have K = -0.4
Finally, the time which the snowball will be completely melted will be when r = 0. So replacing in the equation
![0=-0.4*t+10](https://img.qammunity.org/2020/formulas/mathematics/high-school/2s6w253ks2flpg98t8hzgo58t82ynh8zjt.png)
t = 25 minutes