 # Chapter 10: Surface Area and Volume

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

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

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

Cylinder (bases are circles)
LA = 2∏rh

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

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

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.

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

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

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

Surface Area of a Sphere:

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

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.

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: