Final answer:
To find the volume of a sphere with a radius of 4 units, we use the formula (4/3)πr³, which gives us an unsimplified volume of 256/3π cubic units (approximately 85.33π cubic units). The closest answer choice given is 256π cubic units, although this is not the simplest form and may indicate an error in the provided answer choices.
Step-by-step explanation:
If the sphere has a radius of 4 units, we can find its volume using the formula for the volume of a sphere, which is (4/3)πr³. Plugging the radius into this formula gives us the volume as (4/3)π(4 units)³. To calculate this, we need to cube the radius (4³ = 64) and then multiply by π and 4/3, resulting in the volume of the sphere being (4/3) * 64π cubic units.
So, after the calculation, the volume is (4/3) × 64π = 256/3π cubic units, which simplifies to approximately 85.33π cubic units. However, since this does not match any of the given options, it appears there may be an error in the question or the answer choices. If we disregard the simplification step, the answer closest to the calculated volume is 256π cubic units, which is calculated as (4/3) × 64 × π, but please note that due to an error, this choice is not in its simplest form or is incorrect.