Final answer:
The student's question is related to the mathematics subject, specifically geometry, involving the volume of a sphere. The correct formula for the volume of a sphere is V = (4/3)πr³, which should not be confused with the surface area formula.
Step-by-step explanation:
The question revolves around the mathematical concepts of geometry and specifically deals with the calculation of a sphere's volume. When air is blown into a spherical balloon and you want to calculate how much space it occupies, you use the sphere volume formula: V = (4/3)πr³, where V represents the volume and r is the radius of the sphere.
It's important to note that there's a common confusion between formulas for the volume and the surface area of a sphere. For a sphere with radius r, the formula for volume is indeed V = (4/3)πr³, while the formula for surface area is A = 4πr². Hence, the volume of a sphere is represented by the expression 4πr³/3, not 4πr².
Understanding the correct use of these formulae is essential in various scientific and real-life applications, such as calculating the amount of gas needed to inflate the balloon to a certain size or determining the volume of a celestial body.