1. **Problem Statement:** Label an oblique circular cylinder with a 45 degrees angle with the plane of its base. 2. **Understanding the Problem:** An oblique circular cylinder is a cylinder where the sides are not perpendicular to the base. The angle between the axis of the cylinder and the plane of the base is given as 45 degrees. 3. **Key Concepts:** - The base is a circle. - The axis of the cylinder is tilted at 45 degrees to the base plane. - The height $h$ is the perpendicular distance between the two bases. 4. **Labeling the Cylinder:** - Let the radius of the base be $r$. - Let the height (perpendicular distance between bases) be $h$. - The axis forms a 45 degrees angle with the base plane. 5. **Mathematical Representation:** - The length of the axis $L$ relates to the height $h$ by the angle $\theta=45^\circ$: $$L = \frac{h}{\cos 45^\circ} = h \sqrt{2}$$ 6. **Summary:** - Base radius: $r$ - Height (perpendicular): $h$ - Axis length: $L = h \sqrt{2}$ - Angle between axis and base plane: $45^\circ$ This labeling helps visualize and understand the geometry of the oblique circular cylinder with the specified angle.