Thursday HW Notes



10-1 Notes

Objectives: Classify three-dimensional figures according to their properties.

Use nets and cross sections to analyze three-dimensional figures.

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

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

Examples: Classify the figures. Name the vertices, edges, and bases.

A is a diagram of the surfaces of a three-dimensional figure that can be folded to form the three-dimensional figure. To identify a three-dimensional figure from a net, look at the number of faces and the shape of each face.

Examples: Describe the three-dimensional figure that can be made from the given nets.

A is the intersection of a three-dimensional figure and a plane.

Examples: Describe the cross sections.

Lesson Quiz

1. Classify the figure. Name the vertices, edges, and bases.

2. Describe the three-dimensional figure that can be made from this net.

3. Describe the cross section.

10-2 Notes

Objectives: Draw representations of three-dimensional figures.

Recognize a three dimensional figure from a given representation.

There are many ways to represent a three dimensional object. An ______________________ shows six different views of an object: top, bottom, front, back, left side, and right side.

Example: Draw all six orthographic views of the given object. Assume there are no hidden cubes.

10-4 Notes

Objectives: Learn and apply the formula for the surface area of a prism.

Learn and apply the formula for the surface area of a cylinder.

Prisms and cylinders have 2 congruent parallel bases.

A __________________ is not a base. The edges of the base are called base edges. A ______________ is not an edge of a base. The lateral faces of a _____ ___________ are all rectangles. An ___________ _____________ has at least one nonrectangular lateral face.

An of a prism or cylinder is a perpendicular segment joining the planes of the bases. The height of a three-dimensional figure is the length of an altitude. _________________ is the total area of all faces and curved surfaces of a three-dimensional figure. The ___________________ of a prism is the sum of the areas of the lateral faces.

The net of a right prism can be drawn so that the lateral faces form a ____________ with the same _________ as the prism. The _______ of the rectangle is equal to the _______________ of the base of the prism.

[pic]

The surface area of a right rectangular prism with length ℓ, width w, and height h can be written as

___________________________.

CAUTION!!!!! The surface area formula is only true for _______ prisms. To find the surface area of an oblique prism, add the areas of the faces.

Example: Find the lateral area and surface area of the right rectangular prism. Round to the nearest tenth, if necessary.

Example: Find the lateral area and surface area of a right regular triangular prism with height 20 cm and base edges of length 10 cm. Round to the nearest tenth, if necessary.

The of a cylinder is the curved surface that connects the two bases. The _________ ___________ is the segment with endpoints at the centers of the bases. The axis of a ______________ is perpendicular to its bases. The axis of an ________ ___________ is not perpendicular to its bases. The altitude of a right cylinder is the same length as the axis.

[pic]

[pic]

Example: Find the lateral area and surface area of the right cylinder. Give your answers in terms of (.

Example: Find the lateral area and surface area of a right cylinder with circumference 24( cm and a height equal to half the radius. Give your answers in terms of (.

Example: Find the surface area of the composite figure.

Remember! Always round at the ______ step of the problem. Use the value of ____ given by the ( key on your calculator.

Example: The edge length of the cube is tripled. Describe the effect on the surface area.

Example: A sporting goods company sells tents in two styles, shown below. The sides and floor of each tent are made of nylon. Which tent requires less nylon to manufacture?

Lesson Quiz

Find the lateral area and the surface area of each figure. Round to the nearest tenth, if necessary.

1. a cube with edge length 10 cm

2. a regular hexagonal prism with height 15 in. and base edge length 8 in.

3. a right cylinder with base area 144( cm2 and a height that is 1/3 the radius

4. A cube has edge length 12 cm. If the edge length of the cube is doubled, what happens to the surface area?

5. Find the surface area of the composite figure.

10-5 Notes

Objectives: Learn and apply the formula for the surface area of a pyramid.

Learn and apply the formula for the surface area of a cone.

The is the point opposite the base of the pyramid. The base of a __________________ is a regular polygon, and the lateral faces are congruent isosceles triangles. The ______________________________ is the distance from the vertex to the midpoint of an edge of the base. The ________________________ is the perpendicular segment from the vertex to the plane of the base.

[pic]

The lateral faces of a regular pyramid can be arranged to cover half of a rectangle with a height equal to the slant height of the pyramid. The width of the rectangle is equal to the base perimeter of the pyramid.

[pic]

[pic]

Example: Find the lateral area and surface area of a regular square pyramid with base edge length 14 cm and slant height 25 cm. Round to the nearest tenth, if necessary.

The is the point opposite the base. The is the segment with endpoints at the vertex and the center of the base. The axis of a is perpendicular to the base. The axis of an _________ __________ is not perpendicular to the base.

[pic]

The is the distance from the vertex of a right cone to a point on the edge of the base. The is a perpendicular segment from the vertex of the cone to the plane of the base.

[pic]

Example: Find the lateral area and surface area of a right cone with radius 9 cm and slant height 5 cm.

Example: Find the lateral area and surface area of the cone.

Example: Find the surface area of the composite figure.

[pic]

Lesson Quiz

Find the lateral area and surface area of each figure. Round to the nearest tenth, if necessary.

1. a regular square pyramid with base edge length 9 ft and slant height 12 ft

2. a regular triangular pyramid with base edge length 12 cm and slant height 10 cm

4. A right cone has radius 3 and slant height 5. The radius and slant height are both multiplied by 3/2. Describe the effect on the surface area.

5. Find the surface area of the composite figure. Give your answer in terms of (.

10-6 Notes

Objectives: Learn and apply the formula for the volume of a prism.

Learn and apply the formula for the volume of a cylinder.

The of a three-dimensional figure is the number of nonoverlapping unit cubes of a given size that will exactly fill the interior. Cavalieri’s principle says that if two three-dimensional figures have the same height and have the same cross-sectional area at every level, they have the same volume.

[pic]

[pic]

Example: Find the volume of the prism. Round to the nearest tenth, if necessary.

Example: Find the volume of a cube with edge length 15 in. Round to the nearest tenth, if necessary.

Example: A swimming pool is a rectangular prism. Estimate the volume of water in the pool in gallons when it is completely full (Hint: 1 gallon ≈ 0.134 ft3). The density of water is about 8.33 pounds per gallon. Estimate the weight of the water in pounds.

[pic]

Cavalieri’s principle also relates to cylinders. The two stacks have the same number of CDs, so they have the same volume.

[pic]

Example: Find the volume of the cylinder. Give your answers in terms of ( and rounded to the nearest tenth.

Example: Find the volume of a cylinder with base area 121( cm2 and a height equal to twice the radius. Give your answer in terms of ( and rounded to the nearest tenth.

Example: Find the volume of the composite figure. Round to the nearest tenth.

Lesson Quiz

Find the volume of each figure. Round to the nearest tenth, if necessary.

1. a right rectangular prism with length 14 cm, width 11 cm, and height 18 cm

2. a cube with edge length 22 ft

3. a regular hexagonal prism with edge length 10 ft and height 10 ft

4. a cylinder with diameter 16 in. and height 7 in.

5. a cylinder with base area 196( cm2 and a height equal to the diameter

6. The edge length of the cube is tripled. Describe the effect on the volume.

7. Find the volume of the composite figure. Round to the nearest tenth.

10-7 Notes

Objectives: Learn and apply the formula for the volume of a pyramid. Learn and apply the formula for the volume of a cone.

The _______________ of a pyramid is related to the volume of a __________ with the same base and height. The relationship can be verified by dividing a cube into ________ congruent square pyramids, as shown.

The ________ pyramids are congruent, so they have the _______ volume. The volume of each pyramid is one third the volume of the cube.

[pic]

Example: Find the volume a rectangular pyramid with length 11 m, width 18 m, and height 23 m.

Example: Find the volume of the square pyramid with base edge length 9 cm and height 14 cm.

Example: An art gallery is a 6-story square pyramid with base area ½ acre (1 acre = 4840 yd2, 1 story ≈ 10 ft). Estimate the volume in cubic yards and cubic feet.

[pic]

Example: Find the volume of a cone with radius 7 cm and height 15 cm. Give your answers both in terms of ( and rounded to the nearest tenth.

Example: Find the volume of a cone with base circumference 25( in. and a height 2 in. more than twice the radius.

Example: Find the volume of the cones.

Example: Find the volume of the composite figure. Round to the nearest tenth.

Lesson Quiz

Find the volume of each figure. Round to the nearest tenth, if necessary.

1. a rectangular pyramid with length 25 cm, width 17 cm, and height 21 cm

2. a regular triangular pyramid with base edge length 12 in. and height 10 in.

3. a cone with diameter 22 cm and height 30 cm

4. a cone with base circumference 8( m and a height 5 m more than ½ the radius

5. A cone has radius 2 in. and height 7 in. If the radius and height are multiplied by ¼, describe the effect on the volume.

6. Find the volume of the composite figure. Give your answer in terms of (.

For Your Information: Finding the Area of any regular polygon

In order to use the formulas for the area of regular polygons with 5 sides or more, there is a new vocabulary word you must learn: the apothem, which is the distance of the segment that goes from the center of the shape to side and is perpendicular to the side.

If you know the length of the apothem and the side length (or perimeter), you can use the following formulas:

[pic] or [pic] where n = # of sides

You will be expected to know at least 1 of these formulas for the quiz and final!!!

Example: Find the area of a hexagon with side length 5 and apothem length 3.

-----------------------

M

A right prism and an oblique prism with the same base and height have the same volume.

................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download