Answer:
0.0884 cm/min
Explanation:
Assume that the snowball is perfectly spherical and is melting uniformly from all directions. Then we can use the following formula for calculating surface area from radius d
[tex]A = 4\pi (d/2)^2 = 4\pi d^2/4 = d^2\pi[/tex]
To find the rate of change of diameter, we can apply the chain rule
[tex]\frac{\delta A}{\delta t} = \frac{\delta A}{\delta d}\frac{\delta d}{\delta t}[/tex]
where [tex]\frac{\delta A}{\delta t} = 5 cm^2/min[/tex] is the rate of change in surface area and [tex]\frac{\delta d}{\delta t}[/tex] is the rate of change in diameter, which we are looking for:
[tex]\frac{\delta A}{\delta d} = \frac{\delta d^2\pi}{\delta d} = 2d \pi = 2*9*\pi \approx 56.55[/tex]
Therefore
[tex]\frac{\delta d}{\delta t} = \frac{\delta A}{\delta t} / \frac{\delta A}{\delta d} = 5 / 56.55 = 0.0884 cm/min[/tex]
