Question

The function V(r) = ar can be used to find the volume of air inside a soccer ball given its radius. What does 'a' represent in this context?

A) The radius of the soccer ball.
B) The volume of air inside the soccer ball.
C) A constant that depends on the ball's shape and material.
D) The surface area of the soccer ball.

Answer 1

In the volume formula V(r) = ar for a soccer ball, 'a' is a constant that encapsulates factors like (4/3)π and depends on the ball's shape and material.

Step-by-step explanation:

In the function V(r) = ar, where V represents the volume of air inside a soccer ball and r is the radius of the ball, the constant 'a' signifies a specific factor that accounts for the geometric properties of the sphere. When considering the volume of a sphere, the general formula is V = (4/3)πr³. In this case, 'a' would encapsulate the (4/3)π part of the formula, which remains constant and relates to the shape and material of the ball, making C) A constant that depends on the ball's shape and material the correct answer.