1. a)Sketch the region bounded by the lines y = 3, y = 1, x = 1, x = 6.
The height of a cylinder is five times the radius. If the surface area of the cylinder is 108 ft2, find the radius. 2.
a)Sketch the region bounded by the lines y = 3, y = 1, x = 1, x = 6.
b) Find the perimeter of the region.
 c) Find the area of the region.
 d) Describe the geometric solid formed
by rotating the region about the x-axis
and find its volume
r = 3

2. Homework 9. 100 m² 200 in³ 10. 14, 10  Cylinder with its core missing
, 10
Cylinder with its core missing 40
200 in³ 
2200¶ ~6911 cm³
r=3
198 sq cm
32¶, 40 ¶

3. Chapter 12 Surface Area and Volume of Solids
12.3 Surface area of Pyramids & Cones

4. Formulas: Surface Area of Pyramids: Surface Area of Cones:
Lateral Area of Pyramids: Lateral Area of Cones:

5. Example 1: Use the Pythagorean theorem to find the slant height.8
Use the Pythagorean theorem to find the slant height.
= l 2
Area of each lateral face = ½ bl
A = ½ (16)(17)
A = 8(17)
A =136 sq cm
= l 2
289 = l 2
17 = l

6. Example 2:
B = ½ aP
B = ½ (5√3)(60)
B = 150√3

7. A _______ has a circular base and a ____________ that is not in the same plane as the base. The radius of the base is the radius of the cone.
In a ______________, the segment joining the vertex and the center of the base is perpendicular to the base and the slant height is the distance between the vertex and a point on the base edge.
Cone
Vertex
Right Cone

8. Example 3:
r = 5
l = ?
= l2
= l2
61 = l2
l = 7.81

9. Chapter 12 Surface Area and Volume of Solids
12.5 Volume of Pyramids and Cones

10. Formulas:
Volume of a pyramid: Volume of a cone:

11. Example 3:

12. Pre AP Homework
Daily check
Worksheet 12.3_12.5 More Practice