A cube is ins tuned in a cylinder with radius 5. What is the volume of the cube?

Question

There is nothing that I can add it is a word problem

Answer 1

It is not clear what your question is here.  What do you mean by "ins tuned"?  Assuming you meant inscribed, I'd say looking at a cross section of the cylinder and the cube we would see a square inside of a circle.  Now we need to find the length of a side of this square.  We look at half of the square and see that it would be a 45-45-90 triangle with the long side having the length of the diameter of the circle, 10.  A 45-45-90 triangle has a special relationship between its sides, namely, that hypotenuse = leg * √2.  So the length of the leg is 10 / √2 = 7.071.  Therefore the volume of the cube is 7.071³ = 353.553.

Answer 2

V_cylinder = (4/3)π(5)³