Final answer:
The volume of the space between the sphere and the cube with 14-inch edges is approximately 1307.24 cubic inches, calculated by subtracting the volume of the sphere from the volume of the cube.
Step-by-step explanation:
The question asked is about calculating the volume of the space between a sphere that fits snugly inside a cube with 14-inch edges. To find this, we first calculate the volume of the cube, then the volume of the sphere, and subtract the latter from the former.
Volume of the Cube
Given that the cube has edges of 14 inches, we use the cube volume formula:
Volume of cube = (s)³
where s is the side length of the cube.
Volume of cube = (14)³ = 2744 cubic inches
Volume of the Sphere
Since the sphere fits snugly inside the cube, its diameter is equal to the side length of the cube, which means its radius r is half of that, so 7 inches. The volume of a sphere is given by:
Volume of sphere = 4/3 (pi) (r)³ = 4/3 * π * (7)³ ≈ 1436.76 cubic inches
Volume of Space between Sphere and Cube
To find the space between the sphere and cube, we subtract the volume of the sphere from the volume of the cube:
Space volume = Volume of cube - Volume of sphere ≈ 2744 - 1436.76 ≈ 1307.24 cubic inches