The radius of a spherical balloon is increasing at when the radius is

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

Problem

The radius of a spherical balloon is increasing at

3\,\text{cm s}^{-1}

when the radius is

10\,\text{cm}

. What is the rate at which its volume is increasing at that instant? (a)

2400\pi\,\text{cm}^{3}\text{s}^{-1}

(b)

1200\pi\,\text{cm}^{3}\text{s}^{-1}

(c)

400\pi\,\text{cm}^{3}\text{s}^{-1}

(d)

900\pi\,\text{cm}^{3}\text{s}^{-1}