For a sphere

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

Problem

For a sphere, the radius is given by

r(t)=4t^{2}+1

, where

t

is measured in seconds and

r

in centimeters. What is

\dfrac{dV}{dt}

t=2\text{ s}

, where

V

is the sphere’s volume? (a)

1\,156\pi\text{ cm}^{3}/\text{s}

(b)

4\,624\pi\text{ cm}^{3}/\text{s}

(c)

18\,496\pi\text{ cm}^{3}/\text{s}

(d)

5\,184\pi\text{ cm}^{3}/\text{s}