Rotation of 2-D Figures into 3-D

Rotation of 2-D Figures into 3-D

2-D Figures vs. 3-D Figures A Two-Dimensional (2D) shape is a shape that only has two dimensions: width and height. Examples: Squares, Circles, Triangles, etc. A Three-Dimensional (3D) shape is a shape that has three dimensions: width, depth and height. Examples: Cube, Cylinder, etc.

2D 3D Three-Dimensional figures can be generated by rotating two-dimensional figures. "Rotation" means turning around a center. A three-dimensional object always rotates around an imaginary line called a rotation axis.

WHAT 3D SHAPE IS PRODUCED IF WE ROTATE A RIGHT TRIANGLE ?

WHAT DID YOU GUESS? If you guessed CONE, you are correct! A cone is a solid revolution of a right triangle around one of its legs.

WHAT 3D SHAPE IS PRODUCED IF WE ROTATE A SEMI-CIRCLE ?

WHAT 3D SHAPE IS PRODUCED IF WE ROTATE A SEMI-CIRCLE ? A SPHERE is a solid revolution of a semi-circle around its diameter.

ON YOUR OWN: Given the shape below, determine the 3D solid formed by rotating the two-dimensional shape about the line given. 1. 2.

You try: Given the shape below, determine the 3D solid formed by rotating the two-dimensional shape about the line given. 1. A square rotated about the above line results in a right cylinder. 2. A circle rotated about the above line results in a sphere.

Another Way to Visualize the Rotation If you do not want to cut out the shapes, and you still need help visualizing the rotation: 1. Draw your shape and shade the region to be rotated. 2. Next, draw a reflection (mirror image) of the region about the axis or line of rotation. 3. Connect the vertices of the original image and its reflection using curved lines