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PRISMS

PRISMS. PARTS of a PRISM. FACE. BASE. HEIGHT. FACE. BASE. HEIGHT. TOTAL SURFACE AREA. The sum of the areas of each face. T.A. = ph + 2B p = perimeter of the base h = height of the prism. VOLUME of a PRISM. V = Bh B = area of the Base h = height of the prism.

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PRISMS

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  1. PRISMS

  2. PARTS of a PRISM FACE BASE HEIGHT FACE BASE HEIGHT

  3. TOTAL SURFACE AREA The sum of the areas of each face. T.A. = ph + 2B p = perimeter of the base h = height of the prism

  4. VOLUME of a PRISM V = Bh B = area of the Base h = height of the prism

  5. A right triangular prism is shown. Find the total surface area since the volume = 315. T.A. = ph + 2B V= Bh = 315 p = 10.5 + 7 + 6.5 V= (½·10.5·4)h = 315 h = 15 B =½·10.5·4 = 21 V= 21h = 315 T.A. = 24(15) + 2(21) h = 15 T.A. = 402

  6. Parts of a Pyramid

  7. SLANT HEIGHT • The height of the isosceles triangular lateral face

  8. Examples of Pyramids SLANT HEIGHT

  9. TOTAL SURFACE AREA T.A. = ½pl + B p= perimeter of the base l = slant height B = area of the base

  10. VOLUME of a Pyramid V = ⅓Bh B = Area of the base h = height of the pyramid

  11. T.A. = ½pl + B V = ⅓Bh V = ⅓Bh p = 14(4) = 56 l = 24 B = 14(14) = 196 • Find the total surface area and volume of the pyramid. ⅓(196)(20) B = 14 (14) = 196 1306.66666 h = 20 T.A. = ½(56)(24) + 196 = 868 24 m 20 m 25 m

  12. Cylinders Base is always a circle

  13. Parts of a CYLINDER

  14. TOTAL SURFACE AREA T.A. = 2пrh + 2B r = radius of the base h = height of the cylinder B= area of the base

  15. VOLUME of a Cylinder V = пr2h r = radius of the base h = height of the cylinder

  16. Find the total surface area and volume. 7 in V = πr 2h T.A. = 2пrh + 2B V = π(7) 2 (24) h = 24 24 in r = 7 V = 1176 π B = πr2= π(7)2 = 49π T.A. = 2π(7)(24) + 2(49π) T.A. = 336π + 98π = 434π

  17. CONES

  18. TOTAL SURFACE AREA T.A. = пrl + B r = radius of the base l = slant height of the cone B= area of the base

  19. VOLUME of a Cone V = ⅓пr2h r = radius of the base h = height of the cone

  20. Find the total surface area and volume. V = ⅓πr2h T.A. =πrl + B V = ⅓π(82)15 B = 82 π = 64π 17 meters V = 320π T.A. = π(8)(17) + 64π T.A. = 136π + 64π T.A. =200π 16 meters

  21. Spheres

  22. TOTAL AREA T.A. = 4пr2 r = radius of the sphere

  23. VOLUME of a Sphere V = 4/3 пr3 r = radius of the sphere

  24. A basketball has a diameter of about 9 inches. What is the total area and volume of the basketball? T.A. = 4πr2 T.A. = 4π(9/2)2 T.A. = 81π V = 4/3 πr3 V = 4/3 π(9/2)3 V = 121.5π

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