The temperature at the surface of an inflating balloon is given by

MATHEMATICS · Single correct · CBSE · Mathematics · Applications of Derivatives · Applications of Derivatives

Problem

T(V)=100\sqrt{V}

, where

T

is measured in degrees Celsius and

V

(in cubic meters) is the balloon’s volume. The balloon remains spherical so that

V=\dfrac{4}{3}\pi r^{3}

, where

r(t)

, in meters, is the radius at time

t

(in seconds). When

r=5\text{ m}

and the radius is increasing at

0.20\text{ m/s}

, which of the following is closest to

\dfrac{dT}{dt}

? (a)

7.1\times10^{2}\;^{\circ}\!\text{C/s}

(b)

2.2\times10^{1}\;^{\circ}\!\text{C/s}

(c)

1.4\times10^{2}\;^{\circ}\!\text{C/s}

(d)

1.4\times10^{3}\;^{\circ}\!\text{C/s}