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M3: Sections 10.5 – 10.9 Notes Page 1 of 18 Academic Pre-Algebra Geometry Notes Sections 10.5 – 10.9 Name___________________Pd._____

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M3: Sections 10.5 – 10.9 Notes Page 1 of 18

Academic Pre-Algebra

Geometry NotesSections 10.5 – 10.9

Name___________________Pd._____

Vocabulary ListSections 10.5 – 10.9

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M3: Sections 10.5 – 10.9 Notes Page 2 of 18

Solid

Faces

Prism

Pyramid

Cylinder

Cone

Edges

Vertices

Surface area

Net

Lateral surface

Lateral area

Cross-section

Sphere

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M3: Sections 10.5 – 10.9 Notes Page 3 of 18

Solids

Learning Goal: We will identify types of solids and analyze the intersections of planes and solids to describe the cross sections formed.

CLASSIFYING SOLIDS:

Solid –

Faces –

Example 1: Classify the solid as a prism, pyramid, cylinder, or cone.

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M3: Sections 10.5 – 10.9 Notes Page 4 of 18

COUNTING FACES, EDGES, AND VERTICES

Vocabulary:

Edges – the segments where the faces of a prism or pyramid meet

Vertices – the points where the edges of a prism or pyramid meet

Example 2: Count the number of faces, edges, and vertices in a triangular pyramid.

ON YOUR OWN:Count the number of faces, edges, and vertices in a rectangular prism.

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M3: Sections 10.5 – 10.9 Notes Page 5 of 18

Cross-section – the 2-dimensional figure obtained by a solid’s intersection with a plane

3 Different ways to show a rectangular cross section:

Shown below is the intersection of a plane with a rectangular prism, where face ABCD is a square.

Plane R is perpendicular to face ABCD.

EXAMPLE 3: Identifying Shapes of Cross-SectionsWhich 2-dimensional shape depicts the cross-section shown above?

What if the plane had intersected the rectangular prism parallel to the square face?

ON YOUR OWN:

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M3: Sections 10.5 – 10.9 Notes Page 6 of 18

Use the name of a polygon to describe each cross section of the cube. Points M, N, P, Q, and R are midpoints of edges.

1. Through M, P, Q, and R

2. Through E, A, C, and G

3. Through B, E, and G

4. Through M, N, D, and B

EXTRA PRACTICE:

4. If the rectangular pyramid above is sliced by a plane parallel to the base, which of the following best describes the cross-section of the pyramid? (Note: The rectangular base is not a square.)

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M3: Sections 10.5 – 10.9 Notes Page 7 of 18

Section 10.5: Surface Areas of Prisms and Cylinders

Learning Goal: We will find the surface areas of prisms and cylinders.

Vocabulary:

Surface area –

Net –

Example 1: Use a Net to Find Surface Area

Example 2: Find the surface area of the prism.a. b.

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M3: Sections 10.5 – 10.9 Notes Page 8 of 18

Example 3: Find the Surface Area of a Triangular PrismFind the surface area of the prism.

ON YOUR OWN:Find the surface area of the prism.a. b.

Vocabulary: Lateral surface –

Lateral area –

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M3: Sections 10.5 – 10.9 Notes Page 9 of 18

Example 3: Using a Formula to Find Surface AreaFind the surface area of the cylinder.

ON YOUR OWN:Find the surface area. Use 3.14 for π. Round your answer to the nearest tenth.

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M3: Sections 10.5 – 10.9 Notes Page 10 of 18

Extra Practice:

3.

Section 10.7: Volumes of Prisms and Cylinders

Learning Goal: We will find the volumes of prisms and cylinders.

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M3: Sections 10.5 – 10.9 Notes Page 11 of 18

Example 1: Finding the Volume of a Rectangular PrismFind the volume of the prism.

a. b.

Example 2: Finding the Volume of a Triangular Prisma. b.

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M3: Sections 10.5 – 10.9 Notes Page 12 of 18

Example 3: Finding the Volume of a CylinderFind the volume of the cylinder. Round to the nearest tenth.

ON YOUR OWN:At a state fair, a vendor sells cashew nuts in a plastic cylinder that is 36 inches long and has a diameter of 2 inches. Find the volume of the cylinder. Round to the nearest whole number.

Example 3: Finding the Volume of a Solid

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M3: Sections 10.5 – 10.9 Notes Page 13 of 18

EXTRA PRACTICE:

Section 10.8: Volume of Cones

Learning Goal: We will find the volume of cones.

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M3: Sections 10.5 – 10.9 Notes Page 14 of 18

Example 1: Finding the Volume of a Conea. Find the volume of the

cone shown. Round to the nearest cubic millimeter.

b. Find the volume. Use 3.14 for π. Round to the nearest whole number.

ON YOUR OWN:Find the volume of a cone with a radius 5 centimeters and a height 15 centimeters. Use 3.14 for π. Round to the nearest cubic centimeter.

Example 2: Finding the Volume of a SolidThe grain silo shown is composed of a cylinder and a cone. Find the volume of the silo to the nearest cubic foot. Use 3.14 for π.

ON YOUR OWN:The solid is a cone with a cone-shaped hole in it. Find the volume of the solid. Round your answer to the nearest whole number. Use 3.14 for π.

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M3: Sections 10.5 – 10.9 Notes Page 15 of 18

EXAMPLE 3: Finding an Unknown DimensionFind the dimension of the cone if its volume is 12.4π ft3. Round to the nearest whole number.

ON YOUR OWN:Find the unknown measure. Round to the nearest whole number.

EXTRA PRACTICE:A cone has a height of 3 feet. The radius of the base is 4 feet. What is the approximate volume of the cone?

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M3: Sections 10.5 – 10.9 Notes Page 16 of 18

Volume of Spheres

Learning Goal: We will find the volume of spheres.

Vocabulary: Sphere – the set of all points in space that are a given

distance from a given point called the center.

Volume of a SphereThe volume of a spherical object can be found using the formula

where r is the radius of the sphere.

Example 1: Finding the Volume of a Sphere

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M3: Sections 10.5 – 10.9 Notes Page 17 of 18

a. What is the volume of the sphere to the nearest tenth if its radius is 6 inches? Use 3.14 for π.

b. The diameter of a pearl is 8 millimeters. What is the volume of the pearl to the nearest whole number?

ON YOUR OWN:The diameter of an inflatable beach ball is 3 feet. What is the volume to the nearest whole number?

Example 2: Real World Problem SolvingYou build a snowman statue with snow spheres. What is the volume of the bottom sphere if its diameter is 3 feet? Use 3.14 for π and round to the nearest tenth.

ON YOUR OWN:The radius of a women’s basketball is 4.5 inches. What is the volume of the spherical basketball to the nearest whole number?

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M3: Sections 10.5 – 10.9 Notes Page 18 of 18

Critical Thinking: Describe the possible cross sections of a sphere.