Volume of Solids
Presentation
•
Mathematics
•
12th Grade - University
•
Hard
James Gonzalez
FREE Resource
7 Slides • 10 Questions
1
Volume of solids of revolution
In this activity we will try to understand solids of revolution.
2
Multiple Choice
if this triangle is rotated about the x axis, what figure is formed?
3
Multiple Choice
what figure was rotated about the y axis to produce this cylinder?
4
https://www.onlinemathlearning.com/volume-of-a-cylinder.html
5
Multiple Choice
what is the volume of this cylinder?
6
Multiple Choice
what figure is formed when this circle is rotated around the x axis?
7
Multiple Choice
what common object would resemble this circle rotated around the x axis?
8
Multiple Choice
what common object would resemble the shaded region rotated around the x axis?
9
Multiple Choice
what common object would resemble this region rotated around the y axis?
10
Let´s visualize in 3D
We are going to use the geogebra applet for solids of revolution and confirm what we answered in the previous two questions.
https://www.geogebra.org/classic/BZWTCPfde
11
In the geogebra applet enter:
Functions:
anda=0
b=2
Rotate about horizontal line y=0.
Slide to form solid.
Take time to play with it and discover the solid.
12
Multiple Choice
13
Let´s make some changes:
Functions:
anda=0
b=2
Rotate about vertical line x=0.
Slide to form solid.
Take time to play with it and discover the solid.
14
Multiple Choice
15
This last one:
Functions:
anda=0
b=2
Rotate about vertical line x=0.
Slide to form solid.
Take time to play with it and discover the solid.
16
Multiple Choice
17
We have discovered solids of revolution!
Volume of solids of revolution
In this activity we will try to understand solids of revolution.
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