Final answer:
The volume of a sphere with a great circle circumference of 20π is found by first determining the radius from the circumference, then using the volume formula for a sphere. The calculated volume is (160π³/3), corresponding to Option B.
Step-by-step explanation:
The student's question is regarding the volume of a sphere given the circumference of its great circle is 20π. To find the volume, we need to first calculate the radius of the sphere. The formula for the circumference (C) of a circle is C = 2πr, where r is the radius. Using this formula, we can solve for r given C = 20π, resulting in r = 10.
Once we know the radius, we can calculate the volume (V) using the formula for the volume of a sphere, which is V = (4/3)πr³. Substituting the value of r = 10 into the formula yields V = (4/3)π(10)³ = (4/3)π(1000) = (4000/3)π. Therefore, the correct answer is Option B, which represents the volume (160π³/3).