Math Question: A spherical snowball is being made so that its volume is increasing at the rate of 8 cubic feet per minute. Find the rate at which the radius is increasing when the snowball is 4 feet in diameter?

I set these up this way. What do we know? dV/dt = 8 ft^3/min What do we want? dr/dt = ??? When: when d = 4 feet, r = 2 feet Equation relating V and r? V = 4pir^3/3 Rate equation - implicitly differentiate: d/dt(V) = d/dt(4pi*r^3/3) dV/dt = 4pi r^2 dr/dt Plug in the known values and solve for dr/dt. 8 = 4pi (2)^2 dr/dt 8 = 16pi dr/dt dr/dt = 1/(2pi) = 0.159 ft/min
Answered On 04/25/2020 01:20