Question

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.

Answer 1

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