Volume of Solids

Volume of solids of revolution

In this activity we will try to understand solids of revolution.

Multiple Choice

if this triangle is rotated about the x axis, what figure is formed?

• pyramid

• cylinder

• cone

• frustum

Multiple Choice

what figure was rotated about the y axis to produce this cylinder?

• cylinder

• rectangle

• square

• triangle

https://www.onlinemathlearning.com/volume-of-a-cylinder.html

Multiple Choice

what is the volume of this cylinder?

• 113.04 u³

• 37.68 u³

• 24 u³

• 12 u³

Multiple Choice

what figure is formed when this circle is rotated around the x axis?

• frustum

• circle

• sphere

• cylinder

Multiple Choice

what common object would resemble this circle rotated around the x axis?

• ball

• can

• donut

• lamp

Multiple Choice

what common object would resemble the shaded region rotated around the x axis?

• cone

• can

• donut

• lamp

Multiple Choice

what common object would resemble this region rotated around the y axis?

• mountain

• cone

• flower vase

• lamp

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

In the geogebra applet enter:

• Functions:

   $f\left(x\right)=x^{2\ }+2$ and   $g\left(x\right)=0$ 

• a=0

• b=2

• Rotate about horizontal line y=0.

• Slide to form solid.

• Take time to play with it and discover the solid.

Multiple Choice

If we slice the previous solid, making cuts perpendicular to the x-axis. What shape would we get?

• triangles

• parabolas

• discs

• washers

Let´s make some changes:

• Functions:

   $f\left(x\right)=x^{2\ }+2$ and   $g\left(x\right)=\frac{x^4}{4}+2$ 

• a=0

• b=2

• Rotate about vertical line x=0.

• Slide to form solid.

• Take time to play with it and discover the solid.

Multiple Choice

If we slice the previous solid, making cuts perpendicular to the y-axis. What shape would we get?

• triangles

• parabolas

• discs

• washers

This last one:

• Functions:

   $f\left(x\right)=x^{2\ }+2$ and   $g\left(x\right)=0$ 

• a=0

• b=2

• Rotate about vertical line x=0.

• Slide to form solid.

• Take time to play with it and discover the solid.

Multiple Choice

If we slice the previous solid, making cuts perpendicular to the y-axis. What shape would we get?

• parabolas

• discs

• washers

• washers and discs

We have discovered solids of revolution!