Unit 1, Lesson 2
Solids of Rotation
Integrated Math 3
2.1
Warm-up
Which three go together? Why do they go together?
A
B
C
D
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Which three go together? Why do they go together?
A
B
C
D
Draw the two-dimensional shape that, when rotated around the given axis of rotation, produces each solid of rotation. Ignore any non-symmetric aspects of the solid.
Imagine a coin spinning on its edge. If the coin moves fast enough and stays vertical it would look like a sphere.
This triangular flag is made of metal. What shape will it make if the pole is spun quickly?
When the flag rotates around the pole, we can see a cone.
In both pictures, the object spins around a line called the axis of rotation, and that spinning creates a solid of rotation. When the flag spins around a different axis of rotation, it would make a different solid of rotation. This is what it looks like when the flag is rotated using a different axis of rotation.
A machine called a lathe cuts away at a rotating block of material. For example, a lathe could be used to make a decorative sculpture shaped like the figure on the right from a block of wood. The image on the left shows the cross-sectional shape that would remain after the lathe carved away part of the spinning block of wood. If we rotate this two-dimensional shape using the vertical axis shown, it produces the sculpture shape.
An axis of rotation is a line that a two-dimensional figure is rotated around to produce a three-dimensional figure, called a solid of rotation.
In this diagram, the dashed line is the axis of rotation for the solid of rotation formed by rotating the green triangle.
A solid of rotation is a three-dimensional figure formed by rotating a two-dimensional figure around a line called the axis of rotation.
In this diagram, the axis of rotation is the dashed line. The green triangle is rotated around the axis of rotation to form a solid of rotation.