A snowball melts so that its surface area decreases at a rate of 1cm^2/min. Find a rate at which the diameter decreases when then diameter is 10 cm.

The formula for of a ball is:

S = 4*r^2*pi

or if we express diameter in it:

S = D^2*pi because D=r/2

S1-S2 = (D1^2 - D2^2) * pi

1 = (100 - D2^2) * 3,1415

100-D2^2 = 1/3.1415

D2^2 = 100-1/3.1415

D2 = 9.984cm

which means that Diameter will decrease by rate of:

0.016cm/min