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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.

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**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

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**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

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**Cylinder (bases are circles)**

LA = 2∏rh

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**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

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**Surface Area of Cylinders:**

SA= 2∏rh + 2∏r2

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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.

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

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**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

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**Total Surface Area of Pyramids and Cones:**

Pyramid: SA = LA + B B= area of the base Cone: SA = LA + ∏r2

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**Surface Area of a Sphere:**

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

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**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.

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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:

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