Final answer:
To find the volume of a sphere without a cylinder, use the formula V = (4/3)πr³, where r is the radius of the sphere. Given the equation x²+y²+z²=16 for the sphere, substitute the value of r and calculate the volume. The answer is c) 128π cubic units.
Step-by-step explanation:
To find the volume of a sphere without a cylinder, we can use the formula V = (4/3)πr³, where r is the radius of the sphere.
Given the equation x²+y²+z²=16 for the sphere, we can see that the radius is √16 = 4 units.
Substituting the value of r into the volume formula, V = (4/3)π(4)³ = 256/3π cubic units.
Therefore, the correct answer is c) 128π cubic units.