Warm Up Find the missing side length of each right triangle with legs a and b and hypotenuse c. 1. a...
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![Page 1: Warm Up Find the missing side length of each right triangle with legs a and b and hypotenuse c. 1. a = 7, b = 24 2. c = 15, a = 9 3. b = 40, c = 41 4.](https://reader036.fdocuments.in/reader036/viewer/2022062322/5697bf8a1a28abf838c8a6af/html5/thumbnails/1.jpg)
Warm UpFind the missing side length of each right triangle with legs a and b and hypotenuse c.
1. a = 7, b = 24
2. c = 15, a = 9
3. b = 40, c = 41
4. a = 5, b = 5
5. a = 4, c = 8
c = 25
b = 12
a = 9
![Page 2: Warm Up Find the missing side length of each right triangle with legs a and b and hypotenuse c. 1. a = 7, b = 24 2. c = 15, a = 9 3. b = 40, c = 41 4.](https://reader036.fdocuments.in/reader036/viewer/2022062322/5697bf8a1a28abf838c8a6af/html5/thumbnails/2.jpg)
Surface Areas and Volumes of Pyramids and Cones
Sections 12-5, 12-6, 13-2
![Page 3: Warm Up Find the missing side length of each right triangle with legs a and b and hypotenuse c. 1. a = 7, b = 24 2. c = 15, a = 9 3. b = 40, c = 41 4.](https://reader036.fdocuments.in/reader036/viewer/2022062322/5697bf8a1a28abf838c8a6af/html5/thumbnails/3.jpg)
Pyramids• The slant height of a regular pyramid is the
distance from the vertex to the midpoint of an edge of the base.
• The altitude of a pyramid is the perpendicular segment from the vertex to the plane of the base.
![Page 4: Warm Up Find the missing side length of each right triangle with legs a and b and hypotenuse c. 1. a = 7, b = 24 2. c = 15, a = 9 3. b = 40, c = 41 4.](https://reader036.fdocuments.in/reader036/viewer/2022062322/5697bf8a1a28abf838c8a6af/html5/thumbnails/4.jpg)
Lateral and Surface Areas of Pyramids
• 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.
• L = ½Pl and SA = ½Pl + B
![Page 5: Warm Up Find the missing side length of each right triangle with legs a and b and hypotenuse c. 1. a = 7, b = 24 2. c = 15, a = 9 3. b = 40, c = 41 4.](https://reader036.fdocuments.in/reader036/viewer/2022062322/5697bf8a1a28abf838c8a6af/html5/thumbnails/5.jpg)
Example: Finding Lateral Area and Surface Area of Pyramids
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.
![Page 6: Warm Up Find the missing side length of each right triangle with legs a and b and hypotenuse c. 1. a = 7, b = 24 2. c = 15, a = 9 3. b = 40, c = 41 4.](https://reader036.fdocuments.in/reader036/viewer/2022062322/5697bf8a1a28abf838c8a6af/html5/thumbnails/6.jpg)
Cones• The axis of a cone is the segment with endpoints at
the vertex and the center of the base.• The axis of a right cone is perpendicular to the base.• The axis of an oblique cone is not perpendicular to
the base.
![Page 7: Warm Up Find the missing side length of each right triangle with legs a and b and hypotenuse c. 1. a = 7, b = 24 2. c = 15, a = 9 3. b = 40, c = 41 4.](https://reader036.fdocuments.in/reader036/viewer/2022062322/5697bf8a1a28abf838c8a6af/html5/thumbnails/7.jpg)
Lateral and Surface Areas of Cones
• The slant height of a right cone is the distance from the vertex of a right cone to a point on the edge of the base.
• The altitude of a cone is a perpendicular segment from the vertex of the cone to the plane of the base.
• L = ½Pl and SA = ½Pl + B
![Page 8: Warm Up Find the missing side length of each right triangle with legs a and b and hypotenuse c. 1. a = 7, b = 24 2. c = 15, a = 9 3. b = 40, c = 41 4.](https://reader036.fdocuments.in/reader036/viewer/2022062322/5697bf8a1a28abf838c8a6af/html5/thumbnails/8.jpg)
Example: Finding Lateral Area and Surface Area of Right Cones
Find the lateral area and surface area of the cone.
![Page 9: Warm Up Find the missing side length of each right triangle with legs a and b and hypotenuse c. 1. a = 7, b = 24 2. c = 15, a = 9 3. b = 40, c = 41 4.](https://reader036.fdocuments.in/reader036/viewer/2022062322/5697bf8a1a28abf838c8a6af/html5/thumbnails/9.jpg)
Example:
Find the lateral area and surface area of the right cone.
![Page 10: Warm Up Find the missing side length of each right triangle with legs a and b and hypotenuse c. 1. a = 7, b = 24 2. c = 15, a = 9 3. b = 40, c = 41 4.](https://reader036.fdocuments.in/reader036/viewer/2022062322/5697bf8a1a28abf838c8a6af/html5/thumbnails/10.jpg)
Volume of Pyramids and Cones
![Page 11: Warm Up Find the missing side length of each right triangle with legs a and b and hypotenuse c. 1. a = 7, b = 24 2. c = 15, a = 9 3. b = 40, c = 41 4.](https://reader036.fdocuments.in/reader036/viewer/2022062322/5697bf8a1a28abf838c8a6af/html5/thumbnails/11.jpg)
Example: Finding Volumes of Pyramids
Find the volume of the square pyramid with base edge length 9 cm and height 14 cm.
![Page 12: Warm Up Find the missing side length of each right triangle with legs a and b and hypotenuse c. 1. a = 7, b = 24 2. c = 15, a = 9 3. b = 40, c = 41 4.](https://reader036.fdocuments.in/reader036/viewer/2022062322/5697bf8a1a28abf838c8a6af/html5/thumbnails/12.jpg)
Example: Finding Volumes of Cones
Find the volume of a cone.
![Page 13: Warm Up Find the missing side length of each right triangle with legs a and b and hypotenuse c. 1. a = 7, b = 24 2. c = 15, a = 9 3. b = 40, c = 41 4.](https://reader036.fdocuments.in/reader036/viewer/2022062322/5697bf8a1a28abf838c8a6af/html5/thumbnails/13.jpg)
Example 3
Find the volume of the cone.
![Page 14: Warm Up Find the missing side length of each right triangle with legs a and b and hypotenuse c. 1. a = 7, b = 24 2. c = 15, a = 9 3. b = 40, c = 41 4.](https://reader036.fdocuments.in/reader036/viewer/2022062322/5697bf8a1a28abf838c8a6af/html5/thumbnails/14.jpg)
Lesson Quiz:
Find the volume of each figure. Round to the nearest tenth, if necessary.
1. a rectangular prism with length 25 cm,
width 17 cm, and height 21 cm
2. a cone with diameter 22 cm and height 30 cm
3. a cone with base circumference 8 m and a
height of 7 m
4. a square pyramid with a base side length of
12 m and a height of 15 m
V = 8925 cm3
V = 3801.3 cm3
V = 117.3 3
V = 720 m3