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Chapter 10: Surface Area and Volume

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

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Chapter 10: Surface Area and Volume

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  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: • 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: • 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 baseCone: Square Pyramid: Sphere:

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