Asked by Chris
Gas is escaping a round balloon at2units^2/min.How fast is the surface area shrinking when the radius is 12units?
Answers
Answered by
Damon
Volume = V = (4/3) pi r^3
area =A = 4 pi r^2
r = (A/4pi)^.5
so
V = (4/3) pi (A/4pi)^1.5
dV/dt = (4/3)(1/5)(A/4pi)^.5 (dA/dt/4pi)
here dV/dt = -2
r = 12 so A = 4 pi(144)
solve for dA/dt
area =A = 4 pi r^2
r = (A/4pi)^.5
so
V = (4/3) pi (A/4pi)^1.5
dV/dt = (4/3)(1/5)(A/4pi)^.5 (dA/dt/4pi)
here dV/dt = -2
r = 12 so A = 4 pi(144)
solve for dA/dt