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?

Answer 1

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