The temperature (in °C) inside a solid cube is given by

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

Problem

T(V)=5+0.02V^{3}

, where

V

is the volume in cubic centimeters. The volume depends on the edge length

s

(in centimeters) by

V=s^{3}

. When

s=4\text{ cm}

and increasing at

0.30\text{ cm/min}

, what is

\dfrac{dT}{dt}

? (a)

1.18\times10^{4}\;\text{°C/min}

(b)

3.54\times10^{3}\;\text{°C/min}

(c)

-3.54\times10^{3}\;\text{°C/min}

(d)

7.4\times10^{2}\;\text{°C/min}