Presentations: June 7 June 6 June 5

**Monday**

Notes and practice: Equation of a circle

**Tuesday**

Review and practice: Equation of a circle

**Wednesday**

Review for test

**Thursday**

Test on circles

**Friday**

Review for final

Here is a quick explanation for the formula of the volume of a sphere. This is based on the proof known to the Ancient Greeks.

For this, consider three objects:

- A cylinder;
- A cone with the point on the bottom;
- A hemisphere with the flat side down.

Each object has a height of r and a radius of r.

Take a slice of each object at some height h. The exposed surface (cross-section) will be a circle.

For the cylinder, the radius of this exposed circle will be r, because the radii of all circular cross-sections is r. So the area of the circle for the cylinder at height h is πr^{2}.

For the cone, the radius of this exposed circle will be h, so the area is πh^{2}.

By definition, each point on the hemisphere is r units away from the center. Each point on the exposed circle is at a height of h. Using the Pythagorean Theorem, the radius of the exposed circle is the square root of (r^{2}-h^{2}), so the area is π(r^{2}-h^{2}).

Note that this is the difference between the cylinder and the cone: This is the key.

Since, for each cross-section of the three objects, the area for the cylinder is equal to that of the cone plus that of the hemisphere, it must be the case that the volume of a cylinder is equal to the volume of a cone and the volume of a hemisphere, when all objects have the same radius and height.

We know the formula for the volume of a cylinder: πr^{2}h. If h = r, then πr^{3}.

We know the volume of a cone is one-third of this, so the volume of a hemisphere is two-thirds of this, 2πr^{3}/3. The volume of a sphere is twice that of a hemisphere, that is, 4πr^{3}/3.

Presentations: May 19 May 18 May 17 May 16 May 15

**Monday**

Practice: Naming arcs, arc measures, and lengths

Discussion: Finding pi using the perimeter of polygons

**Tuesday**

Notes and practice: Area of Circles and Sectors

**Wednesday**

Practice: Area of Circles and Sectors, review all unit material

**Thursday**

Notes and Practice: Area of a sphere (review: cylinder and cone)

**Friday**

Practice: All unit material

Quiz

Notes: Circle tangents

Presentations: May 5 May 4 May 3 May 2 May 1

**Monday**

Review: Area of Triangles and Quadrilaterals

Notes: Area of Regular Polygons

**Tuesday**

Review and practice: Area of Regular Polygons

**Wednesday**

Review for Quiz

Quiz

**Thursday**

Notes and practice: Volume of Prisms and Cylinders

**Friday**

Review and practice: Volume of Prisms and Cylinders

Notes: Volume of Pyramids and Cones

Presentations: April 28 April 27 April 26 April 25 April 24

**Monday**

Review for Chapter 8 Test

**Tuesday**

Chapter 8 Test

**Wednesday**

Notes: Area of Parallelograms and Triangles

**Thursday**

Review and practice: Area of Parallelograms and Triangles

Notes: Area of Trapezoids, Rhombuses, and Kites

**Friday**

Review and practice: Area of Trapezoids, Rhombuses, and Kites

Presentations: April 21 April 20 April 19 April 18 April 17

**Monday**

Review and practice: Pythagorean Theorem and Trig Ratios

**Tuesday**

Notes: Angles of Elevation and Depression

**Wednesday**

Review and practice: Angles of Elevation and Depression

**Thursday**

Notes: The Law of Sines

**Friday**

Review and practice: The Law of Sines