## Homework #5 Question 4

Consider a solid ball of radius . Cut a cylindrical hole, through the center of the ball, such that the remaining body has height . Call this the donut . Use Cavalieri’s principle to calculate the volume of . Calculate the volumes of and .

Several students have asked what looks like. Here are some pictures that I found to illustrate the concept. The donut is the region between the red sphere and blue cylinder. The golden balls below show various views of the donut. The donut should fit between the two planes and , so that it has total height .

## Malin Christersson’s Cube Toy

I was looking through the Geogebra site and found this lovely applet Orthographic Projection by Malin Christersson.

This is a lovely tool for investigating one of my favourite facts about hexagons:

*The area maximizing orthogonal projection of a cube is the regular hexagon*.

It turns out that Malin has tonnes of awesome geometry stuff online!

- Hyperbolic tiler!
- Pythagora’s Tree!
- A whole Tumblr full of great animations!

Awesome math art!

## Public Talks for UTSC

## MAT 134 — Post-Term Test #1 Survey

Thank you for filling out MAT 134 Post-Term Test #1 Survey.

Here is what Parker learned about the class!

## String Figure Poster Sketch

We’re almost ready for our final string figure presentation on May 2nd.

Now we just have to put it all together!

## The String Figure Mentorship

This week at the string mentorship we played with some nice figures. From left to right we are: Caroline Graham with Jacob’s Ladder, Parker Glynn-Adey a variant of the Well, Hillarey Tsui with Crow’s Feet, and Jacob Kikukawa with Wawu from Nauru Island.

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