Asked by ssss
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?
Answers
Answered by
Reiny
..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
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
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