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7.1 – 7.2 Surface Area & Volume of Prisms

7.1 – 7.2 Surface Area & Volume of Prisms. Surface Area & Volume. Surface area: the sum of the areas of all the faces of the figure Measured in square units (units 2 ) Volume: the number of cubes that will fit inside the figure Measured in cubic units (units 3 ). Prisms.

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7.1 – 7.2 Surface Area & Volume of Prisms

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  1. 7.1 – 7.2Surface Area & Volume of Prisms

  2. Surface Area & Volume • Surface area: the sum of the areas of all the faces of the figure • Measured in square units (units2) • Volume: the number of cubes that will fit inside the figure • Measured in cubic units (units3)

  3. Prisms • Prisms are polyhedra that have two polygon bases connected by quadrilateral faces. • They are named by the shape of their bases • If the prism is slanted it is oblique • If it is not slanted it is right

  4. Oblique (just lean, man)

  5. “Oblique”

  6. Bonaventura Cavalieri (1598-1647) •  Italian mathematician who was a student of Galileo. In 1635, he stated Cavalieri's Principle, which states that if two solids have the same height, and if their cross sections taken parallel to and at equal distances from their bases are always equal, then the solids have the same volume. This was a stepping stone towards calculus! • This only works for VOLUME!

  7. Handsome! (and smart, too)

  8. Has the volume changed?

  9. We usually deal with RIGHT prisms

  10. Volume of a right prism • Volume: • Find the area of the base • Find the distance from one base to the next (height) • Multiply the area of the base times the height

  11. Volume of any prism • V = Bh • B is the area of one base • h is the height of the prism Volume of a prism = area of 1 prism base x prism height

  12. HINT • IF YOU ALREADY SEE BIG “B” • THEN BE HAPPY! (because someone has already found the area of the base for you)

  13. SA & Vol. of Prisms • Formulas for Rectangular Prisms • SA = 2lw + 2wh + 2lh • V = lwh • Formulas for Cubes • SA = 6s2 • V = s3

  14. Surface Area of a Right Prism • Surface Area: • Break the prism apart into all the faces (unfold it in your head) • Find the area of each face • Add the areas together

  15. Surface Area of a Right Prism • SA = L + 2B • L is the lateral area (the area of the rectangular faces) • B is the area of one base (they’re congruent, so double it)

  16. Surface area of a right prism • You may also use this formula: • SA = hp + 2B • where h = the height of the prism • and p = the perimeter of the base • What does “B” stand for?

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