Golden Spheres

let $\large n$ be the maximum number of golden spheres that can be made

then, we have

$\large n=\dfrac{volume~of~cube}{volume~of~sphere}=\dfrac{x^3}{\frac{4}{3}\pi (r^3)}=\dfrac{10^3}{\frac{4}{3}\pi (2^3)}=\dfrac{1000}{33.51032} \approx$ $\color{#D61F06}\boxed{\large 29}$

The volume of the cube is $C = 10^{3} = 1000 \text{ cm}^{3}$ .
The volume of one sphere is $S =$ $\dfrac{ 4 } { 3 } \pi r^{3} =$ $\dfrac{ 4 } {3} \pi \times (2^{3} ) =$ $\dfrac{ 32 \pi}{3 } \text{ cm}^{3}$ .

The maximum number of spheres that can be made from the cube are $\left \lfloor \dfrac{ C} {S} \right \rfloor =$ $\left \lfloor \dfrac{ 1000 } { \frac{32 \pi}{3} } \right \rfloor =$ $\left \lfloor \dfrac{ 3000 } { 32 \pi } \right \rfloor =$ $\lfloor 29.84 \ldots \rfloor = \boxed{ 29 }$ $_\square$

The volume of a cube is given by $v=a^3$ where $a$ is the edge length of the cube. The volume of a sphere is given by $v=\dfrac{4}{3}\pi r^3$ where $r$ is the radius of the sphere.

$\color{#3D99F6}\text{number of spheres}=\dfrac{\text{volume of the cube}}{\text{volume of one sphere}}=\dfrac{10^3}{\frac{4}{3}\pi (2^3)} = \color{#D61F06}\boxed{29}$

The maximum number of spheres $=floor(1000/( \dfrac {4} {3} \pi\times 2^{3}))=floor(29.84....)=29.$