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 calculate the volume of the balloon using the formula for the volume of a sphere: \[ V = \frac{4}{3} \pi r^3 \] Substituting the radius \( r = 9 \) meters: \[ V = \frac{4}{3} \pi (9)^3 = \frac{4}{3} \pi (729) \approx 3053.63 \, \text{cubic meters} \] Next, we can find the weight of the air by multiplying the volume by the density: \[ \text{Weight} = V \times \text{density} = 3053.63 \, \text{cubic meters} \times 0.9 \, \text{kg/m}^3 \approx 2748.27 \, \text{kg} \] Rounding to the nearest integer, the weight of the air that Ariah needs to fill the balloon is approximately **2748 kg**.