1. Chapter 10: Surface Area and Volume
Objectives: Students will be able to find the surface area and volume of three dimensional figures.

2. Prism: 2 congruent, parallel faces (called the bases).
The other faces of the prism are called lateral faces
Named by the shape of its base
Altitude: perpendicular segment joining the bases
Height: the length of the altitude

3. Lateral Surface Area: For a Right Prism: LA = ph p=perimeter of base
The sum of the areas of the lateral faces
Area of the sides (not including the bases)
For a Right Prism:
LA = ph
p=perimeter of base
h= height

4. Cylinder (bases are circles)
LA = 2∏rh

5. Surface Area: For a Right Prism: SA= LA + 2B B= area of the base
Sum of lateral surface area and the area of the 2 bases
Find lateral surface area and then add the area of the bases
For a Right Prism:
SA= LA + 2B
B= area of the base

6. Surface Area of Cylinders:
SA= 2∏rh + 2∏r2

7. Pyramids and Cones
Pyramid: The base is any polygon and the other faces (lateral faces) are triangles that meet at a common vertex Cone: Pyramid whose base is a circle.

8. Slant Height (l):
The length of the altitude of the lateral face of the pyramid

9. Lateral Surface Area of Pyramids and Cones:
Lateral Surface Area of Pyramid: LA = ½ pl p= perimeter of base l= slant height Lateral Surface Area of Cone: LA = ∏rl

10. Total Surface Area of Pyramids and Cones:
Pyramid: SA = LA + B B= area of the base Cone: SA = LA + ∏r2

11. Surface Area of a Sphere:

12. Cross Section
The shape you get when you “slice” a 3 dimensional figure

13. VOLUME The space that a figure occupies Measured in cubic units
When finding volume of pyramids and cones, need to use the height, not slant height. The height is perpendicular to the base.

14. VOLUME FORMULAS:
Right Rectangular Prism: Any Pyramid: V= lwh Any Right Prism: B = area of the base V= Bh B= area of the base Cone: Square Pyramid: Sphere: