Final answer:
The volume of a sphere inscribed in a cube with an edge length of 8 inches is approximately 268.1 cubic inches when rounded to the nearest tenth.
Step-by-step explanation:
To find the volume of the sphere that is inscribed in the cube with an edge length of 8 inches, we first need to determine the radius of the sphere. Since the sphere fits exactly inside the cube, its diameter is equal to the edge length of the cube, which means the radius is half of that length. Therefore, the radius (r) is 4 inches.
The formula for the volume of a sphere is V = 4/3 π r3. Using the radius we found:
V = 4/3 π (4 inches)3
V = 4/3 π (64 cubic inches)
V = (256/3) π cubic inches
V ≈ 268.1 cubic inches (rounded to the nearest tenth)
Therefore, the volume of the sphere is approximately 268.1 cubic inches.