Show:
Spindle Torus
Horn Torus
Ring Torus
Formulas
Name that Torus!
100
True or false: A spindle torus intersects itself.
False: A spindle torus meets itself at point (0,0,0)
100
True or False: A horn torus has a tiny hole in the center of the shape at point (0,0,0).
False. A horn torus fills the entire volume of the shape.
100
True or False: Ring torus should never be assumed unless specified.
False: Ring torus is assumed if no specification is given
100
True or False: Lowercase "r" is used into tori formulae to represent the tube that forms the torus shape.
True! Capitol R is used for the radius of the circle shape of the torus itself.
100
This torus is the shape of a bagel.
Ring torus!
200
Fill in the blank: A spindle torus ______ itself at point (0,0,0)
A spindle torus meets itself at point (0,0,0)
200
Fill in the blank: A Horn Torus ________ itself inside the shape.
A horn torus intersects itself inside the shape
200
Based on what we have learned, how do we know that a ring torus is not a polygon? (Multiple answers acceptable)
A ring torus does not have straight sides, angles, or vertices.
200
What is the formula for volume of a torus?
2π^2Rr^2
200
This torus is the shape of a red blood cell.
Horn Torus!
300
Which axis can you rotate a circle around to form a torus?
You can rotate a circle around the z-axis to form a torus.
300
Fill in the blank: When split in half, horn tori are always _________
When split in half, horn tori are always symmetrical
300
If a circle does not touch nor contain point (0,0) and is then rotated around the z-axis, does it form a ring torus?
Yes, because the resulting torus would be a circular tube with a hole in the middle.
300
What is the formula for surface area of a torus?
4π^2Rr
300
This torus is frequently found in nature as the center of symmetry for many three dimensional objects.
Spindle Torus!
400
What is the volume of a spindle torus where R=5 and r=2.5? (Round to the nearest hundredth)
616.85 units cubed.
400
What is the volume of a horn torus when R=6 and r=3.4? (Round to the nearest hundredth)
1,369.11 units cubed
400
Find the surface area of a ring torus when R=10 and r=3.5. (Round to the nearest hundredth)
1,381.74 units squared
400
A torus with R=6 and r=3 must be what kind of torus?
It must be a spindle torus, because the opposite radii of the tubes add up to the total radius of the torus, so they would meet at point (0,0,0).