4. (12 points) The coordinate axes form the axes of three right circular cylinders with radius 1 . Find the volume of the solid that is common to the three cylinders.

Step 1 ：The problem is asking for the volume of the solid that is common to three cylinders. The three cylinders are formed by the coordinate axes, and each has a radius of 1. This means that the solid common to all three cylinders is an octant of a sphere with radius 1.

Step 2 ：The volume of a sphere is given by the formula \((4/3)\pi r^3\), and an octant of a sphere is 1/8 of the total volume.

Step 3 ：Therefore, the volume of the solid common to the three cylinders is \((1/8)*(4/3)\pi(1)^3 = (1/2)\pi\).

Step 4 ：Substituting the value of r = 1, we get the volume of the sphere as \(V_{sphere} = 4.1887902047863905\)

Step 5 ：The volume of the octant is then \(V_{octant} = 0.5235987755982988\)

Step 6 ：Final Answer: The volume of the solid that is common to the three cylinders is \(\boxed{0.524}\)