draw the solid of revolution obtained by rotating the given plane region about line l.\nwhich figure below…

Answer:

C. The third figure (frustum-like shape with a cylindrical hole)

Explanation:

Step1: Identify the plane region

The region is a right triangle with one vertical side parallel to, but not touching, the axis of revolution $L$.

Step2: Analyze the rotation of vertices

Rotating the top-left vertex around $L$ creates a circle; rotating the bottom-left vertex creates a larger circle below it.

Step3: Determine the inner boundary

Since the vertical side of the triangle is at a constant distance from $L$, it generates a cylindrical inner surface.

Step4: Determine the outer boundary

The hypotenuse of the triangle is slanted, so its rotation generates a conical outer surface (a frustum).

Step5: Select the matching solid

The resulting solid is a frustum with a cylindrical hole through the center, which matches figure C.