Final answer:
To determine how many breaths Jesse takes to fill a balloon, calculate the volume of the balloon using the diameter and divide by the volume Jesse can fill per breath, rounding to the nearest whole number.
Step-by-step explanation:
To calculate the number of breaths Jesse takes to fill a balloon, we need to first find the volume of a full balloon using the given diameter (24 cm). The formula for the volume of a sphere is V = \frac{4}{3}\pi r^3, where r is the radius of the sphere. Since the diameter of the balloon is 24 cm, the radius is half of that, which is 12 cm. Plugging the radius into the formula, we get V = \frac{4}{3} \pi (12 cm)^3.
The next step is to divide the total volume of the balloon by the volume of air Jesse can fill per breath (820 cm^3) to find out how many breaths are needed. Assuming Jesse inflates the balloon completely, her breath filling capacity will determine the total number of breaths required to fill the balloon. We must round the final answer to a whole number of breaths as partial breaths are not possible in this context.