The equation V=43πr3

Question

represents the relationship between the volume of a sphere and its radius. What does the end behavior tell you about the relationship between the volume of the sphere and its radius?(1 point)
Responses

As the radius increases to infinity, the volume of the sphere will decrease to negative infinity.
As the radius increases to infinity, the volume of the sphere will decrease to negative infinity.

As the radius decreases to negative infinity, the volume of the sphere will increase to infinity.
As the radius decreases to negative infinity, the volume of the sphere will increase to infinity.

As the radius decreases to negative infinity, the volume of the sphere will remain constant.
As the radius decreases to negative infinity, the volume of the sphere will remain constant.

As the radius increases to infinity, the volume of the sphere will increase to infinity.
As the radius increases to infinity, the volume of the sphere will increase to infinity.
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Answer 1

The equation \( V = 43\pi r^3 \) describes how the volume \( V \) of a sphere changes with its radius \( r \).

To analyze the end behavior of this equation:

• As the radius \( r \) increases towards infinity (\( r \to \infty \)), the term \( r^3 \) also increases towards infinity. Consequently, the volume \( V \) will also increase towards infinity.

Therefore, the correct statement regarding the end behavior is:

As the radius increases to infinity, the volume of the sphere will increase to infinity.