Jesse is filling spherical balloons. When full, one of these balloons has a diameter of 24 cm . Jesse can fill a balloon at a rate of \( 820 \mathrm{~cm}^{3} \) per breath. How many breaths does it take Jesse to fill a balloon? Round to a whole breath.

To find out how many breaths it takes to fill the balloon, we first need to calculate the volume of the balloon. The formula for the volume \( V \) of a sphere is given by: \[ V = \frac{4}{3} \pi r^3 \] The radius \( r \) of the balloon is half of the diameter, so: \[ r = \frac{24 \text{ cm}}{2} = 12 \text{ cm} \] Now, substituting \( r \) into the volume formula: \[ V = \frac{4}{3} \pi (12 \text{ cm})^3 \approx \frac{4}{3} \pi (1728 \text{ cm}^3) \approx 7238.23 \text{ cm}^3 \] Next, we divide the total volume by the volume filled per breath: \[ \text{Number of breaths} = \frac{7238.23 \text{ cm}^3}{820 \text{ cm}^3} \approx 8.83 \] Rounding to the nearest whole number means it takes Jesse approximately **9 breaths** to fill the balloon.