Question

A sphere of radius $3$, inscribed in a cube, is tangent to all six faces of the cube. The volume contained outside the sphere and inside the cube, in standard units, is:

• A. $97$
• B. $103$
• C. $109$
• D. $115$

Answer 1

The correct option is B $103$

Volume of sphere is $\frac{4}{3}\times \pi r^3=\pi \times \frac{4}{3}\times 3^3=36\pi =113.14$
Length of cube is equal to diameter of circle, which implies $a=6$
Volume of cube is equal to $a^3=6^3=216$
Remaining volume is $216-113.14\approx 103$