Question

which plane figure generates a cylinder when it rotates about the dashed line? a.

Explanation:

Step1: Recall the concept of solid of revolution

A cylinder is formed by rotating a rectangle (or a right - angled parallelogram) about one of its sides. When a rectangle rotates about one of its vertical (or horizontal) sides, the side about which it rotates becomes the axis of the cylinder, and the length and width of the rectangle become the height and the radius (or vice - versa) of the cylinder. If we consider a circle, rotating a circle about a line that is not its diameter (for example, a line parallel to a tangent of the circle) will not form a cylinder. But if we have a rectangle, when rotated about one of its sides, each point of the rectangle moves in a circular path, and the set of all these circular paths forms a cylinder.

Step2: Analyze the options (assuming the options include a rectangle and other figures like circle, triangle, etc.)

If option A is a rectangle (since the problem is about generating a cylinder), when we rotate the rectangle about the dashed line (which should be one of its sides), the rectangle will sweep out a cylinder. A circle rotated about a diameter gives a sphere, a triangle rotated about an axis can give a cone or a frustum (depending on the triangle and the axis), but a rectangle rotated about one of its sides gives a cylinder.

Answer:

(Assuming the correct option is the one with a rectangle, for example, if option A is a rectangle) A. [Rectangle (the plane figure that generates a cylinder on rotation about the dashed line)]