1. **Problem Statement:** Find the maximum number of hemispheres that can be scooped from a cube. 2. **Understanding the problem:** We want to fit hemispheres inside a cube such that the hemispheres do not overlap and are fully contained within the cube. 3. **Key formula and rules:** - The volume of a cube with side length $s$ is $V_{cube} = s^3$. - The volume of a hemisphere with radius $r$ is $V_{hemisphere} = \frac{2}{3} \pi r^3$. - To maximize the number of hemispheres, we need to consider how many hemispheres can fit inside the cube without overlapping. 4. **Assumptions:** - The hemispheres are placed with their flat faces on the cube's faces or inside the cube. - The radius $r$ of each hemisphere must be such that the hemisphere fits inside the cube. 5. **Finding the maximum radius:** - The largest hemisphere that fits inside the cube has radius $r = \frac{s}{2}$ because the diameter must be less than or equal to the cube's side length. 6. **Packing hemispheres:** - To maximize the number of hemispheres, consider placing them in a grid arrangement inside the cube. - Each hemisphere occupies a cube of side length equal to its diameter $2r$. 7. **Calculating the number of hemispheres:** - Number of hemispheres along one edge: $n = \left\lfloor \frac{s}{2r} \right\rfloor$. - Since $r = \frac{s}{2}$, $2r = s$, so $n = \left\lfloor \frac{s}{s} \right\rfloor = 1$. 8. **Conclusion:** - Only one hemisphere of radius $\frac{s}{2}$ can fit inside the cube. - If smaller hemispheres are used, more can fit, but the problem does not specify the radius. **Final answer:** The maximum number of hemispheres that can be scooped from the cube is 1 if the hemisphere radius is half the cube's side length.