Geometry Unit 10 & 11 Note Sheets 1 Date Name of Lesson 10.1 Areas of Parallelograms, Triangles 10.2 Areas of Trapezoids, Rhombi and Kites 10.3 Area of Circles and Sectors 10.4 Areas of Regular Polygons and Composite Figures 10.5 Area of Nonrigid Transformations 10.6 Surface Area 11.1 Cross Section and Solids of Revolution 11.2 Volume of Prisms and Cylinders 11.3 Volume of Pyramids and Cones 11.4 Volume of Spheres 11.6 Volume of Nonrigid transformations 11.7 Applying Measurements
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Geometry Unit 10 & 11 Note Sheets Date Name of …...Geometry Unit 10 & 11 Note Sheets 1 Date Name of Lesson 10.1 Areas of Parallelograms, Triangles 10.2 Areas of Trapezoids, Rhombi
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Geometry Unit 10 & 11 Note Sheets
1
Date Name of Lesson
10.1 Areas of Parallelograms, Triangles
10.2 Areas of Trapezoids, Rhombi and Kites
10.3 Area of Circles and Sectors
10.4 Areas of Regular Polygons and Composite Figures
10.5 Area of Nonrigid Transformations
10.6 Surface Area
11.1 Cross Section and Solids of Revolution
11.2 Volume of Prisms and Cylinders
11.3 Volume of Pyramids and Cones
11.4 Volume of Spheres
11.6 Volume of Nonrigid transformations
11.7 Applying Measurements
Geometry Unit 10 & 11 Note Sheets
2
Area of Figures Review
Circle Sector of a Circle Parallelogram Triangle Trapezoid Rhombi and Kites
r – radius
d -diameter
r – radius
x – degree of
sector
A-area of sector
𝐴 = 𝜋𝑟2
𝐶 = 2𝜋𝑟
𝐶 = 𝑑𝜋
Proportion: 𝐴
𝜋𝑟2=
𝑥
360°
Equation:
𝐴 =𝑥
360°𝜋𝑟2
𝐴 = 𝑏ℎ
𝐴 =1
2𝑏ℎ
𝐴1
2(𝑏1 + 𝑏2)ℎ
𝑑1, 𝑑2: 𝐷𝑖𝑎𝑔𝑜𝑛𝑎𝑙𝑠
𝐴 =1
2𝑑1𝑑2
Geometry Unit 10 & 11 Note Sheets
3
Surface Area of Figures Prism Cylinder Pyramid Cone
Example 2: The surface area of a small pyramid is 40 square centimeters. If the scale factor between the
small pyramid and a larger pyramid is𝟏
𝟑 , what is the surface area of the larger pyramid?
Guided Practice 2: Two similar cones have radii of 5 inches and
15 inches. What is the ratio of the volume of the smaller cone to the volume of the larger cone?
Example 3: Circular cone A and circular cone B are similar. The cones have radii of 10 millimeters and
15 millimeters, respectively. The volume of cone A is approximately 1047.2 cubic millimeters. Find the
volume of cone B.
Guided Practice 3: SOFTBALLS The softballs shown are similar spheres. If the radius of the larger
softball is 1.9 inches, find the radius of the smaller softball.
Example 4: CONTAINERS The containers below are similar cylinders. Find the height h of the smaller
container.
Geometry Unit 10 & 11 Note Sheets
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11.7 Applying Measurements
Example 1: A. Find the population density of Rhode Island to
the nearest tenth.
B. Find the population of Delaware, given that the
Population density is 379.7 persons/mi. Example 2: A rectangular state park with a length of 2.7 miles and a width of 2.5 miles has a duck population of 2500 ducks. The park rangers want to build a new playground, but can only build the playground if the duck population density is greater than 420 ducks per square mile. Does the population density allow for the playground to be built?
Geometry Unit 10 & 11 Note Sheets
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Example 3: A sphere has a radius of 3 feet. Its mass is 550 grams. Find the density of the sphere to the nearest tenth. Example 4: An artist is making a sculpture in the shape of a rectangular prism that is 3 meters long, 180 centimeters wide, and 0.5 meter tall. She wants to be sure that the finished sculpture has a density less than 1.5 grams per cubic centimeter. If she makes the sculpture with clay, it will have a mass of 3780 kilograms. If she makes the sculpture with glass, it will have a mass of 6,480,000 grams. Which material should she use?