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Our learning goal is to be able to solve for perimeter, area and volume. Learning Goal Assignments Perimeter and Area of Rectangles and Parallelograms Perimeter and Area of Triangles and Trapezoids The Pythagorean Theorem Circles Drawing Three-Dimensional figures - PowerPoint PPT Presentation
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Our learning goal is to be able to solve for perimeter, area and volume.
Learning Goal Assignments1.Perimeter and Area of Rectangles and Parallelograms
2.Perimeter and Area of Triangles and Trapezoids
3.The Pythagorean Theorem
4.Circles
5.Drawing Three-Dimensional figures
6.Volume of Prisms and Cylinders
7.Volume of Pyramids and Cones
8.Surface Area of Prisms and Cylinders
9.Surface Area of Pyramids and Cones
10.Spheres
Pre-Algebra
6-7 Volume of Pyramids and Cones
Learning Goal Assignment
Learn to find the volume of pyramids and cones.
Pre-Algebra
6-7 Volume of Pyramids and Cones
Pre-Algebra HOMEWORK
Page 743
#5-13
Show Work!
Pre-Algebra
6-7 Volume of Pyramids and Cones6-7 Volume of Pyramids and Cones
Pre-Algebra
Warm Up
Problem of the Day
Lesson Presentation
Chapter 6-6 Lesson Quiz
Find the volume of each figure to the nearest tenth. Use 3.14 for .
306 in3942 in3 160.5 in3
No; the volume would be quadrupled because you have to use the square of the radius to find the volume.
10 in.
8.5 in.3 in.
12 in.12 in.
2 in.
15 in.10.7 in.
1. 3.2.
4. Explain whether doubling the radius of the cylinder above will double the volume.
Pre-Algebra
6-7 Volume of Pyramids and Cones
Warm Up
1. Find the volume of a rectangular prism that is 4 in. tall, 16 in. wide and 48 in deep.
2. A cylinder has a height of 4.2 m and a diameter of 0.6 m. To the nearest tenth of a cubic meter, what is the volume of the cylinder? Use 3.14 for .
3. A triangular prism’s base is an equilateral triangle. The sides of the equilateral triangle are 4 ft, and the height of the prism is 8 ft. To the nearest cubic foot, what is the volume of the prism?
3072 in3
1.2 m3
55.4 ft3
Pre-Algebra
6-7 Volume of Pyramids and Cones
Pre-Algebra
6-7 Volume of Pyramids and Cones
Problem of the Day
A ream of paper (500 sheets) forms a rectangular prism 11 in. by 8.5 in. by 2 in. What is the volume of one sheet of paper?0.374 in3
Pre-Algebra
6-7 Volume of Pyramids and Cones
Learning Goal Assignment
Learn to find the volume of pyramids and cones.
Pre-Algebra
6-7 Volume of Pyramids and Cones
Vocabulary
pyramid
cone
Pre-Algebra
6-7 Volume of Pyramids and Cones
A pyramid is named for the shape of its base. The base is a polygon, and all of the other faces are triangles. A cone has a circular base. The height of a pyramid or cone is measured from the highest point to the base along a perpendicular line.
Pre-Algebra
6-7 Volume of Pyramids and Cones
VOLUME OF PYRAMIDS AND CONES
(22)
Pre-Algebra
6-7 Volume of Pyramids and ConesAdditional Example 1A: Finding the Volume of
Pyramids and Cones
Find the volume of the figure.
13V = • 14 • 6
V = 28 cm3
A.
V = Bh13
B = (4 • 7) = 14 cm2 12
Pre-Algebra
6-7 Volume of Pyramids and Cones
Try This: Example 1A
13V = • 17.5 • 7
V 40.8 in3
A.
V = Bh13
B = (5 • 7) = 17.5 in2 12
Find the volume of the figure.
5 in.
7 in.
7 in.
Pre-Algebra
6-7 Volume of Pyramids and ConesAdditional Example 1B: Finding the Volume of
Pyramids and Cones
13V = • 9 • 10
V = 30 94.2 in3
B.
V = Bh13
B = (32) = 9 in2
Use 3.14 for .
Find the volume of the figure.
Pre-Algebra
6-7 Volume of Pyramids and Cones
13V = • 9 • 7
V = 21 65.9 m3
B.
V = Bh13
B = (32) = 9 m2
Use 3.14 for .
Find the volume of the figure.
Try This: Example 1B
7 m
3 m
Pre-Algebra
6-7 Volume of Pyramids and ConesAdditional Example 1C: Finding the Volume of
Pyramids and Cones
13V = • 84 • 10
V = 280 m3
C.
V = Bh13
B = 14 • 6 = 84 m2
Find the volume of the figure.
Pre-Algebra
6-7 Volume of Pyramids and Cones
13V = • 16 • 8
V 42.7 ft3
C.
V = Bh13
B = 4 • 4 = 16 ft2
Find the volume of the figure.
Try This: Example 1C
4 ft4 ft
8 ft
Pre-Algebra
6-7 Volume of Pyramids and ConesAdditional Example 2: Exploring the Effects of Changing
DimensionsA cone has a radius of 3 ft. and a height of 4 ft. Explain whether tripling the height would have the same effect on the volume of the cone as tripling the radius.
When the height of the cone is tripled, the volume is tripled. When the radius is tripled, the volume becomes 9 times the original volume.
Pre-Algebra
6-7 Volume of Pyramids and Cones
Try This: Example 2A cone has a radius of 2 m and a height of 5 m. Explain whether doubling the height would have the same effect on the volume of the cone as doubling the radius.
Double the Radius
Double the Height
Original Dimensions
1
3V = r2h
1
3
1
31
3= (22)5
20.93 m3
1
3V = r2 (2h)
= (22)(2•5) = (2 • 2)2(5)
V = (2r)2h
41.87 m3 83.73 m3
1
3
When the height of a cone is doubled, the volume is doubled. When the radius is doubled the volume is 4 times the original volume.
Pre-Algebra
6-7 Volume of Pyramids and Cones
Additional Example 4: Social Studies Application
The Pyramid of Kukulcán in Mexico is a square pyramid. Its height is 24 m and its base has 55 m sides. Find the volume of the pyramid.
B = 552 = 3025 m2 13
V = (3025)(24)
V = 24,200 m3
A = bh
V = Bh13
Pre-Algebra
6-7 Volume of Pyramids and Cones
Try This: Example 4
B = 482 = 2304 m2 13
V = (2304)(12)
V = 9216 m3
A = bh
V = Bh13
Find the volume of a pyramid with a height of 12 m and a base with 48 m sides.
Pre-Algebra
6-7 Volume of Pyramids and Cones
Lesson Quiz: Part 1
Find the volume of each figure to the nearest tenth.Use 3.14 for .
78.5 in3
6.3 m3
1. the triangular pyramid
2. the cone
Pre-Algebra
6-7 Volume of Pyramids and Cones
Lesson Quiz: Part 2
Find the volume of each figure to the nearest tenth.Use 3.14 for .
Yes; the volume is one-third the product of the base area and the height. So if you triple the height, the product would be tripled.
3. Explain whether tripling the height of a square pyramid would triple the volume.
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