Question
A spherical snowball is uniformly melting art of rate of pi/18 in^3/min. At what rate is its diameter decreasing when its surface area is 3 in^2?
Answers
Steve
a = pi d^2
when a=3, d^2 = 3/pi
v = pi/6 d^3
dv/dt = pi/2 d^2 dd/dt
So,
-pi/18 = pi/2 (3/pi) dd/dt
dd/dt = -pi/27 in/min
when a=3, d^2 = 3/pi
v = pi/6 d^3
dv/dt = pi/2 d^2 dd/dt
So,
-pi/18 = pi/2 (3/pi) dd/dt
dd/dt = -pi/27 in/min