1. Warm Up
Find the surface area and the volume
1. A prism with a length of 8 cm, width of 6 cm and height of 15 cm
SA = 516 cm V = 720 cm3
2. A cylinder with a radius of 12 inches and a height of 20 inches
SA = in2
V = in3

2. Surface Areas and Volumes of Pyramids and Cones

3. Pyramids
The slant height of a regular pyramid is the distance from the vertex to the midpoint of an edge of the base.
The height of a pyramid is the perpendicular segment from the vertex to the plane of the base.

4. Lateral and Surface Areas of Pyramids
The lateral faces of a regular pyramid create four identical triangles with a base of s and a height equal to the slant height of the pyramid.
LA = 2sl
SA = s2+ 2sl

5. 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.
SA = 896 cm2
LA = 700 cm2

6. Example: Finding Lateral Area and Surface Area of Pyramids
Find the lateral area and surface area the pyramid below:
SA = 2225cm2
LA = 1600cm2

7. 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 height of a cone is a perpendicular segment from the vertex of the cone to the plane of the base.

8. Lateral and Surface Areas of Cones
LA = πrl
SA = πr2 + πrl

9. Example: Finding Lateral Area and Surface Area of Right Cones
Find the lateral area and surface area of the cone when: h = 12 cm, r = 9 cm and L = 15 cm.
SA = cm2
LA = cm2

10. Example: Finding Lateral Area and Surface Area of Right Cones
Find the lateral area and surface area of the cone.

11. Volume of Pyramids and Cones

12. Example: Finding Lateral Area and Surface Area of Right Cones
Find the volume of the cone when:
h = 12 cm, r = 9 cm and L = 15 cm.

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

14. Example: Finding Volumes of Pyramids
Find the volume of the pyramid.

15. Example: Finding Volumes of Cones

16. 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 = cm3
V =
V = 720 m3