Final answer:
To find the volume of a sphere with a given surface area of 144 pi square inches, we first solve for the radius and then apply the volume formula. The radius is 6 inches and thus the volume of the sphere is 288 pi cubic inches.
Step-by-step explanation:
The surface area of a sphere is given as 144 pi square inches. To find the volume of the sphere, we first need to determine the radius of the sphere using the formula for the surface area, which is
Surface Area = 4 pi r².
By setting this equal to 144 pi and solving for r, we find that r = 6 inches.
Next, we use the formula for the volume of a sphere, which is Volume = 4/3 pi r³,
substituting r with 6 inches.
Thus, the volume is 4/3 pi (6 inches)³ = 288 pi cubic inches.