The radius of a spherical ice sculpture is decreasing at a rate of

MATHEMATICS · Single correct · A Level · Mathematics · Differentiation · Differentiation

Problem

The radius

r

of a spherical ice sculpture is decreasing at a rate of

0.8\text{ cm/min}

. The surface area

S

of the sculpture is related to

r

S=4\pi r^{2}

, and the temperature

T

of the ice is a differentiable function of

S

. At a moment when

\dfrac{dT}{dS}>0

, which of the following statements about

\dfrac{dT}{dt}

is most accurate? (a)

\displaystyle \frac{dT}{dt}=0

(b)

\displaystyle \frac{dT}{dt}>0

(c)

\displaystyle \frac{dT}{dt}<0

(d) The sign of

\displaystyle \frac{dT}{dt}

cannot be determined from the given information.