Final answer:
To find the volume of a sphere with a surface area of 144π cm², first calculate the radius using the surface area formula, then use this radius in the volume formula to get the volume, which is 288π cm³. Option C is the correct answer.
Step-by-step explanation:
If the surface area of a sphere is 144π cm², we can use the area formula to calculate the radius, and then use the radius to find the volume. The surface area of a sphere is given by 4πr². Setting this equal to 144π, we get 4πr² = 144π. To solve for r², we divide both sides by 4π, resulting in r² = 36. Taking the square root of both sides, we find that r = 6 cm.
Now, to find the volume of the sphere, we use the volume formula, which is V = 4/3πr³. Substituting r = 6 cm into this formula, we get V = 4/3π(6³) = 4/3π(216) = 288π cm³. Therefore, the correct option for the volume of the sphere is C) 288π cm³.