# Volume of Inflating Spherical Balloon as a Function of Time

Date of Exam:

**Problem**

A meteorologist is inflating a spherical balloon with a helium gas. If the radius of a balloon is changing at a rate of 1.5 cm/sec., express the volume *V* of the balloon as a function of time *t* (in seconds). Hint: Use composite function relationship *V*_{sphere} = 4/3 π*r*^{3} as a function of *x* (radius), and *x* (radius) as a function of *t* (time).

A. V(t) = 5/2 πt^{3} |
C. V(t) = 9/2 πt^{3} |

B. V(t) = 7/2 πt^{3} |
D. V(t) = 3/2 πt^{3} |

**Answer Key**

[ C ]

**Solution**

$V = \frac{4}{3}\pi x^3$

$V = \frac{4}{3}\pi (1.5t)^3$

$V = \frac{9}{2}\pi t^3$ ← *answer*

Category: