Question

if the two - dimensional figure is rotated about side, \\( \overline { c d } \\), which of the following three - dimensional shapes is formed by this rotation?
\\( \bigcirc \\) cone
\\( \bigcirc \\) rectangular prism
\\( \bigcirc \\) cylinder
\\( \bigcirc \\) frustum

Explanation:

Step1: Recall rotation - shape relationships

When a two - dimensional figure is rotated about an axis, different 3D shapes are formed. A rectangle (assuming the two - dimensional figure is a rectangle, since rotating about one of its sides \(CD\)) when rotated about one of its sides.

Step2: Analyze the rotation of a rectangle about one of its sides

If we rotate a rectangle about one of its sides, the resulting three - dimensional shape has two circular bases (from the rotation of the opposite side of the rectangle which is perpendicular to the axis of rotation \(CD\)) and a curved lateral surface.

Answer:

cylinder