# Monday, March 6th

In class today students had about 1/2 hour to work silently on the chapter review assignment and then time to compare. I answered questions on a few area problems. One nice question was whether a square peg in a circular hole is a tighter fit than a circular peg in a square hole? The ratio of the area of a square peg to the smallest round hole it can fit through is $\dpi{300}\inline 2 : \pi$ which we can reason must be less than $\dpi{300}\inline 66 \dfrac{2}{3}\%$ while the ratio of the area of the round peg to the smallest square hole's area is $\dpi{300}\inline \pi : 4$ which we can reason is greater than 75%. So, the round peg in a square hole is a tighter fit.

Study Guide

• Be able to explain the area formula for any 3- or 4-sided polygon and also any regular n-gon.
• Explain why the area of a circle is $\dpi{300}\inline \pi r^2$ and the circumference is $\dpi{300}\inline \pi \cdot D$ or $\dpi{300}\inline 2 \pi r$
• Explain why the lateral surface area of any pyramid with a regular polygon base is $\dpi{300}\inline \dfrac{P \cdot l}{2}$
• Explain why the formula for the surface area of a cone is $\dpi{300}\inline \pi r^2 + \pi r l$ or $\dpi{300}\inline \pi r(r + l)$
• Solve problems involving area of geometric shapes, express answers in exact form (in terms of $\dpi{300}\inline \pi$, in simplest radical form, using fractions)
• Understand problems similar to homework problems throughout the unit.

Assignment: Chapter 8 Review on p. 455: 1-47 (odds) + 38. Priority problems (to be done first) were 25, 38, 39, 45.