Final answer:
The air pressure inside the balloon is 1.4 x 10³ Pa (Option A), determined by dividing the force exerted by the air against the balloon walls (45 N) by the calculated surface area of the balloon (314 m²).
Step-by-step explanation:
To calculate the air pressure inside the balloon, we can use the formula for pressure, which is P = F / A, where P is the pressure, F is the force, and A is the area. Given that the force of air against the walls of the balloon is 45 N and the radius of the sphere is 5.0 m, we can first calculate the surface area of the balloon with the provided formula: surface area = 12.56 x radius².
The surface area A = 12.56 x (5.0 m)² = 12.56 x 25 m² = 314 m². Now we can calculate the pressure using the formula P = F / A:
P = 45 N / 314 m² = 0.1433121019 N/m². P can be rounded to three significant figures, which is 0.143 x 10³ N/m², or in terms of the options provided, 1.4 x 10³ Pa, since 1 Pa = 1 N/m². Therefore, the correct answer is A. 1.4 x 10³ Pa.