Question

match the solid below to the two - dimensional shaded region that, upon rotation about the bold axis, would produce the solid. (note: figures not necessarily drawn to scale.)

Explanation:

Step1: Recall the rule of rotation

When a right - triangle rotates around one of its right - sides, it forms a cone. The length of the rotated right - side is the height of the cone, and the length of the other right - side is the radius of the base of the cone.

Step2: Analyze each option

• Option A: When the right - triangle in option A rotates around the vertical axis (one of its right - sides), the vertical side length is \(3\) (height of the cone) and the horizontal side length is \(4\) (radius of the base of the cone), which can form the given cone.
• Option B: Rotating around the non - right - side (the horizontal axis in the figure) will not form a cone with the given height and radius.
• Option C: The lengths of the sides of the triangle do not match the height (\(3\)) and radius (\(4\)) of the cone.
• Option D: The lengths of the sides of the triangle do not match the height (\(3\)) and radius (\(4\)) of the cone.

Answer:

A