Question #5e9cc
2 Answers
The limiting size of cube is the space diagonal from a lower vertex to an upper vertex. We find this using Pythagoras' theorem.
First, the face diagonal is found
Then the space diagonal is
The biggest cube that can therefore be cut from the sphere will have a space diagonal of 5 inches, so
Volume of cube =
Explanation:
Maximum
subjected to
Using Lagrangian multipliers
Stationarity condition
Solving for
so