Three-dimensional figures, or solids, can be made up of flat or curved surfaces. Each flat surface is called a face. An edge is the segment that is the intersection of two faces. A vertex is the point that is the intersection of three or more faces.

A cube is a prism with six square faces A cube is a prism with six square faces. Other prisms and pyramids are named for the shape of their bases.

A Net is a 2D representation of a 3D solid A Net is a 2D representation of a 3D solid. Imagine “unfolding” the solid so you can see all surfaces!

A Cross section is the 2D region describing the intersection of a solid and a plane Complete examples on workbook pgs 455 – 456 Complete workbook pg 460

Cavalieri’s Principal This principal works for all solids This means we can use the same volume formulas for right solids AND oblique solids!

Area and Volume Have your area and volume toolkits ready from here on out. We will be jumping between chapters 10 and 11 for the next few weeks. First, let’s review circles on the Area toolkit!

Section 11-4: Spheres Write these formulas on your volume toolkit and complete the sphere examples

Section 11-2: Cylinders Write these formulas on your volume toolkit and complete the cylinder examples

Section 10-1: Area of Triangles and Quadrilaterals Fill in the diagrams, formulas, and examples on the area toolkit for the following: Rectangle/parallelogram: A = bh Triangle: A = ½bh Trapezoid: A = ½h(b1 + b2) Kite: A = ½d1d2 Rhombus: A = ½d1d2 Remember, quadrilaterals can be divided into triangles. This idea is how you can derive the formulas if you forget them! You can now complete #1 – 17 of the area packet

Section 10-2: Area of Regular Polygons Write this formula on your area toolkit and complete the regular polygon examples Area of a regular polygon: A = ½ aP Think of it as dividing the polygon into isosceles triangles, finding the area of one triangle, and then multiplying by how many triangles you have! You can now complete #18 – 22 of the area packet

Section 11-2: Prisms Write these formulas on your volume toolkit and complete the prism examples

Section 11-3: Pyramids and Cones Write these formulas on your volume toolkit and complete the pyramid and cone examples

Density Density = mass / volume Example 1: What is the density of aluminum if 10.8 grams has a volume of 4cm3? Example 2: Sam is digging for gold and finds 2 pieces of what he thinks is gold. The first piece has a mass of 9.66g and a volume of 0.5cm3. The second piece has a mass of 14.1g and a volume of 0.75cm3. If the density of gold is 19.32 grams/cm3, which piece(s) are real gold? Population density –example 2 on workbook pg 432

Section 10-4: Area and Perimeter on a Coordinate Plane Complete Example 1 from workbook page 431 Complete workbook page 435 #4 – 5

Length, Perimeter, Area, and Volume Ratios If 2 figures are similar, then: Length Ratio = Scale factor Perimeter ratio = Scale factor Area ratio = (Scale factor)2 Volume ratio = (Scale factor)3 The units have the same exponent as the ratio!

Length, Perimeter, Area, and Volume Ratios Example 1: ABCDEF ~ MNOPQR. What is the perimeter and area of MNOPQR? 6 cm P = 36 cm A = 94cm2 A B C D E F 2 cm M O P Q R N

Length, Perimeter, Area, and Volume Ratios Example 2: A cylindrical container has a height of 5in and holds 12 fluid ounces. How many fluid ounces would a similar container hold if the height was increased to 10in?