largest cube that can be cut from a sphere

space diagonal of the cube = diameter of the sphere = 10 inches

let D = space diagonal of the cube

let a = edge length of the cube

Formula: $D=a \sqrt{3}$

So,

$D=a \sqrt{3}$

$10=a \sqrt{3}$

$\left(10=a \sqrt{3}\right)^3$

$a^3=\dfrac{10^3}{(\sqrt{3})^3}$

$\boxed{a^3=192.45 \space \text{in}^3}$