Question

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?

Answer 1

..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