The temperature (in degrees Celsius) at the surface of a melting spherical ice ball is

MATHEMATICS · Single correct · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation

Problem

T(r)=100e^{-0.02r}

, where

r

is the radius in centimeters. The mass

m

of the ice (in grams) satisfies

m=\dfrac{4}{3}\pi\rho r^{3}

with constant density

\rho=1\text{ g/cm}^{3}

. At the instant when

m=600\text{ g}

, the mass is decreasing at a rate of

120\text{ g/min}

. Which of the following is closest to

\dfrac{dT}{dt}

at that instant? (a)

6.3

(b)

0.12

(c)

0.63

(d)

-0.63