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Key Area and Volume Formulas for Geometric Shapes: Triangles, Prisms, Cylinders, and More

This guide provides essential formulas for calculating the surface area and volume of various geometric shapes, including triangles, rectangles, trapezoids, hexagons, right prisms, right cylinders, square pyramids, cones, and spheres. Learn to name the parts of each shape, comprehend how to apply the formulas for surface area (SA) and volume (V), and explore relationships between similar solids through scale, area, and volume ratios. Perfect for students or anyone needing a refresher on geometry essentials!

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Key Area and Volume Formulas for Geometric Shapes: Triangles, Prisms, Cylinders, and More

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  1. Chapter 10

  2. IMPORTANT!From Chapter 7, KNOW area formulas for:TrianglesRectanglesTrapezoidsHexagons

  3. Name the parts: 3 1 2 (Right Rectangular Prism)

  4. 1- lateral edge (height)2- lateral face (side)3- base (top/bottom)

  5. RIGHT PRISM: SA = ( ____ )( ____ ) + 2( ____ )

  6. SA = ph + 2B height Base Area base perimeter

  7. RIGHT PRISM: Volume = ( ____ )( ____ )

  8. V = Bh Base Area height

  9. RIGHT CYLINDER: SA = 2( __ )( __ )( __ ) + 2( __ )( __)

  10. SA = 2πrh + 2πr2

  11. RIGHT CYLINDER: V = ( ____ )( ____ )( ____ )

  12. V = πr2h

  13. Complete:

  14. Name the parts: 1 2 4 3 5 (Square Pyramid)

  15. 1- lateral edge 2- slant height (l) 3- apothem 4- height (h) 5- base edge

  16. PYRAMID: SA = ½ ( ___ )( ___ ) + ( ___ )

  17. SA = ½ pl + B base Area base perimeter

  18. PYRAMID: V = ( ____ )( ____ )

  19. V = Bh Base Area

  20. Name the parts: 3 1 2

  21. 1- height (h) 2- radius (r) 3- slant height (l)

  22. CONES: SA = ( __ )( __ )( __ ) + ( __ )( __ )

  23. SA = π r l + π r2

  24. CONES: V = 1/3 ( ___ )( ___ )( ___ )

  25. V = 1/3 πr2 h volume of a cylinder

  26. Complete the chart:

  27. SPHERES: Area = ( ___ )( ___ )( ___ )

  28. A =4 πr2 Area of a circle

  29. SPHERE: V = ( ___ )( ___ )( ___ )

  30. V =π r3

  31. If r3 = 8 then r = ____If r3 = 27 then r = ____If r3 = 125 then r = ____

  32. If r3 = 8 then r = 2If r3 = 27 then r = 3If r3 = 125 then r = 5

  33. Complete for similar solids: Scale Factor/Similarity Ratio = 2 : 3 Area Ratio = _____ Volume Ratio = _____

  34. Complete for similar solids: Scale Factor/Similarity Ratio = 2 : 3 Area Ratio = 22:32 = 4:9 Volume Ratio = 23:33 = 8:27

  35. Find the slope and y-intercept of the following line:6x – 8y = 15

  36. 6x – 8y = 15-8y = -6x+ 15y = x + slope (3/4) y-intercept (-15/8)

  37. Solve by factoring:x2 – 3x – 10 = 0

  38. x2 – 3x – 10 = 0(x – 5)(x + 2) = 0x = 5, -2

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