calculus
posted by ssss on .
a spherical snowball with diameter 4 inches is removed from the freezer in June and begins melthing uniformly such that it is shrinking 2 cubic inches per minute. How fast ( in square inches per minute) is the surface area decreasing when the radius is 1 inch?

..it is shrinking 2 cubic inches per minute > dV/dt = 2 cubic inches/min
V = (4/3)pi(r^3)
dV/dt = 4pi(r^2)dr/dt
when r  1 and dV/dt = 2
2 = 4pi(1)dr/dt
dr/dt = 1/(2pi)
but A = 4pi(r^2)
then dA/dt = 8pi(r)dr/dt
so again when r=1
dA/dt = 8pi(1)(1/2pi)
=4 square inches/min