Friday, April 14

In class students had time to complete yesterday's assignment and a challenge worksheet also I reviewed with students how to derive the formula for the volume of a sphere. In the proof that $\dpi{300}\inline V_\text{sphere} = \dfrac{4}{3}\pi r^3$ we assume

• Cavalieri's principle: If, in two solids of equal altitude, the sections made by planes parallel to and at the same distance from their respective bases are always equal, then the volumes of the two solids are equal
• $\dpi{300}\inline V_\text{Cylinder} = \pi r^2 \cdot h$
• $\dpi{300}\inline V_\text{Cone} = \dfrac{1}{3} \pi r^2 \cdot h$

In order to be proficient, students should be able to solve volume problems involving spheres and other shapes we have studied. Today's worksheet and the ability to prove the volume of a circle is $\dpi{300}\inline \dfrac{4}{3}\pi r^3$ are both areas in which students can reach the highly proficient level.

Assignment: Complete 10.6: 1-16 and the 10.5/10.6 worksheet handed out today.