A spherical snow ball is melting so that its volume is decreasing at the rate of 8 c.c./sec then the rate of change of radius when the radius is 2 cm, is :

Step-by-step solution

Let V be the volume and r be the radius of the spherical snowball. V = 4 3 r^3 Differentiating with respect to time t : dV dt = 4 r^2 dr dt Given that the volume is decreasing at the rate of 8 c.c./sec, dV dt = -8 cm ^3 /sec. Substituting r = 2 cm and dV dt = -8 : -8 = 4 (2)^2 dr dt -8 = 16 dr dt dr dt = - 1 2 cm/sec The negative sign indicates that the radius is decreasing at the rate of 1 2 cm/s. Answer: The radius is decreasing at the rate of 1 2 cm/s