Final answer:
To calculate the volume of a spherical hot air balloon with a radius of 9 meters, we use the volume formula for spheres, resulting in approximately 3053.08 cubic meters. Using the deflation rate of 22 cubic meters per minute, it will take approximately 138.78 minutes to completely deflate the balloon.
Step-by-step explanation:
Volume of a Spherical Hot Air Balloon
To find the volume of a full spherical hot air balloon, we use the formula V = \(\frac{4}{3}\)\pi r^3, where V is the volume and r is the radius of the sphere. Given that the radius (r) is 9 meters, the volume can be calculated as:
V = \(\frac{4}{3}\)\pi (9)^3
V = \(\frac{4}{3}\) * 3.14 * (9)^3
V = \(\frac{4}{3}\) * 3.14 * 729
V ≈ 3053.08 cubic meters
Time to Deflate the Balloon
To calculate the time it takes to completely deflate the balloon, we use the rate of deflation. Since the rate is 22 cubic meters per minute and the full volume of the balloon is approximately 3053.08 cubic meters, we can set up a proportion.
Time (minutes) = Total Volume / Deflation Rate
Time = 3053.08 / 22
Time ≈ 138.776 minutes
Therefore, it will take approximately 138.78 minutes to completely deflate the balloon.