Question

match the rotations of two - dimensional objects to the three - dimensional objects they form.
right triangle: rotated around one of its legs
rectangle: rotated around one of its sides
circle: rotated around its diameter
cylinder cone sphere

Explanation:

Step1: Analyze rotation of right - triangle

When a right - triangle is rotated around one of its legs, the resulting three - dimensional object is a cone. The leg around which it is rotated becomes the height of the cone, and the other leg becomes the radius of the base of the cone.

Step2: Analyze rotation of rectangle

When a rectangle is rotated around one of its sides, the resulting three - dimensional object is a cylinder. The side around which it is rotated becomes the height of the cylinder, and the adjacent side becomes the radius of the base of the cylinder.

Step3: Analyze rotation of circle

When a circle is rotated around its diameter, the resulting three - dimensional object is a sphere. Every point on the circle is at a fixed distance (the radius) from the diameter (the axis of rotation), and this generates a sphere.

Answer:

right triangle: rotated around one of its legs $\to$ cone; rectangle: rotated around one of its sides $\to$ cylinder; circle: rotated around its diameter $\to$ sphere