The surface area of a spherical balloon is increasing at 50 ,cm /s when its radius is…

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

Problem

The surface area of a spherical balloon is increasing at 50\,cm

^{2}

/s when its radius is 10\,cm. What is the instantaneous rate at which the volume of the balloon is increasing at this moment? (a)

125\,\text{cm}^{3}/\text{s}

(b)

250\pi\,\text{cm}^{3}/\text{s}

(c)

250\,\text{cm}^{3}/\text{s}

(d)

50\,\text{cm}^{3}/\text{s}