Question

1. match the two - dimensional figure and axis of rotation with the solid of rotation that can be formed by rotating the figure using that axis.
2. a cylinder
3. a sphere
4. a cone

a.
image of a right - angled triangle with a dashed vertical line along one of its legs
b.
image of a rectangle with a dashed vertical line along one of its sides
image of a semicircle with a dashed vertical line along its diameter (partially shown)

Explanation:

Step1: Analyze Figure A

Figure A is a right triangle, and when rotated around the vertical dashed axis (one of its legs), the set of all points traced by the hypotenuse forms a cone. So Figure A (right triangle) rotated about the given axis forms a cone (3).

Step2: Analyze Figure B

Figure B is a rectangle, and when rotated around the vertical dashed axis (one of its sides), the set of all points traced by the opposite side forms a cylinder. So Figure B (rectangle) rotated about the given axis forms a cylinder (1).

Step3: Analyze the third figure (semicircle)

The third figure is a semicircle, and when rotated around the vertical dashed axis (its diameter), the set of all points traced by the semicircle forms a sphere. So the semicircle rotated about the given axis forms a sphere (2).

Answer:

A - 3 (a cone), B - 1 (a cylinder), Semicircle - 2 (a sphere) (assuming the third figure is a semicircle for the sphere; if the third figure's label is missing, based on the solids: triangle→cone, rectangle→cylinder, semicircle→sphere)