Ariah has a hot air balloon. When full, the balloon is a sphere with a radius of 9 meters. She fills it with hot air whose density is 0.9 kilograms per cubic meter. Since this is less dense than the air in the atmosphere, the balloon is carried upwards. What is the weight of the air that Ariah needs to fill the balloon? Round your answer, if necessary, to the nearest integer.

To find the weight of the air that Ariah needs to fill the balloon, we first need to calculate the volume of the spherical balloon. The formula for the volume \( V \) of a sphere is: \[ V = \frac{4}{3} \pi r^3 \] where \( r \) is the radius. For Ariah's balloon with a radius of 9 meters: \[ V = \frac{4}{3} \pi (9)^3 \approx \frac{4}{3} \pi (729) \approx 3053.63 \, \text{cubic meters} \] Next, we multiply the volume by the density of the hot air to find the mass: \[ \text{Mass} = V \times \text{Density} = 3053.63 \, \text{m}^3 \times 0.9 \, \text{kg/m}^3 \approx 2748.27 \, \text{kg} \] Since weight is mass times the acceleration due to gravity (approximately \( 9.81 \, \text{m/s}^2 \)), we calculate the weight: \[ \text{Weight} = 2748.27 \, \text{kg} \times 9.81 \, \text{m/s}^2 \approx 26945.37 \, \text{N} \] Rounding to the nearest integer, the weight of the air that Ariah needs to fill the balloon is approximately **26945 N**.