Final answer:
To find the radius of the melting spherical snowball at the moment when the radius is decreasing at a rate of -3/5 inch per minute, we apply related rates using the formula for the volume of a sphere in terms of its radius. We differentiate with respect to time and use the given rates of change to solve for the snowball's radius.
Step-by-step explanation:
To solve the problem of a melting spherical snowball, we apply the relationship between the volume of a sphere and its radius and consider the rate at which these quantities change.
Let's denote the radius of the snowball by r, and the volume by V. The formula for the volume of a sphere is V = (4/3)πr^3. If the volume is decreasing at a constant rate, we're dealing with a case of related rates in calculus where differential calculus is applied to the volume formula. The student is specifically asking for the radius of the snowball when the rate of change of the radius, dr/dt, is -3/5 inches per minute.
We first differentiate the volume with respect to time to obtain the relationship between the rates of change: dV/dt = 4πr^2 (dr/dt). We know the rate of volume change, dV/dt, and the rate of radius change, dr/dt, so we can solve for r.
Once these calculations are complete, we can obtain the radius of the snowball at the given rate of change.