Final answer:
To find the volume of the sphere inscribed in a cube with a volume of 343m³, calculate the cube side length, derive the sphere's radius, and use the volume formula V = 4/3 π r³, which yields approximately 179.594m³.
Step-by-step explanation:
The student asks about the volume of a sphere inscribed inside a cube when the cube's volume is 343m³. First, we find the side length of the cube (s) by taking the cube root of the volume, so s = ∛343m³, which gives us s = 7m. Since the sphere is inscribed in the cube, the diameter of the sphere is equal to the side length of the cube, hence the radius (r) of the sphere is half of that, r = 3.5m. Using the formula for the volume of a sphere V = 4/3 π r³, we plug in the radius to find V = 4/3 π (3.5m)³. Simplifying this we get the volume of the sphere as approximately 179.594m³.