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Surface Area of Prisms and Cylinders

Surface Area of Prisms and Cylinders. Area. The area of a shape is a measure of how much surface the shape takes up. Prisms & Cylinders. Polyhedron – a solid bounded by polygons (a 3D figure). Prism – a polyhedron with two congruent parallel faces called bases.

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Surface Area of Prisms and Cylinders

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  1. Surface Area of Prisms and Cylinders

  2. Area The area of a shape is a measure of how much surface the shape takes up.

  3. Prisms & Cylinders Polyhedron – a solid bounded by polygons (a 3D figure) Prism – a polyhedron with two congruent parallel faces called bases Cylinder – a solid with congruent circular bases that lie in parallel planes radius base base height Lateral face (4) base base

  4. Prisms are classified by the shapes of their bases

  5. Rectangles l w The perimeter of a rectangle with length l and width w can be written as: Perimeter = 2l + 2w or Perimeter = 2(l + w) The area of a rectangle is given as: Area = lw

  6. Triangles The area of a triangle is found by multiplying the base (b) times the height (h) and dividing by 2 (or multiplying by ½):

  7. Surface Area verses Lateral Area of a Prism The lateral area of a polyhedron or prism is the sum of the area of its lateral faces (without getting the area of the bases). LA = Ph P = Perimeter of the base h = height of 3-D shape base Lateral face (4) base

  8. Surface Area verses Lateral Area of a Prism • The surface area of a polyhedron or prism is the sum of area of its faces (including the area of the bases). • SA = Ph + 2B P = Perimeter of the base • h = height of 3-D shape • B = Area of the base base Lateral face (4) base

  9. Example

  10. Example

  11. The circumference of a circle circumference diameter = π For any circle, The Circumference is found through the formula: C = πd Inversely, if you have the circumference, you can find the diameter through the formula:

  12. Formula for the area of a circle We can find the area of a circle using the formula Area of a circle = π×r×r or radius Area of a circle = πr2

  13. Surface Area verses Lateral Area of a Cylinder The lateral area of a cylinder is the area of its curved surface. LA = r = radius of the base h = height of 3-D shape radius base height base

  14. Surface Area verses Lateral Area of a Cylinder • The surface area of a cylinder is equal to the sum of the lateral area and the areas of the two bases. • SA = radius base height base

  15. Scaling If we scale the dimensions of a prism or any other 3D figure, we are multiplying each dimension (length, width, height, etc) by the scale factor. For example, if we have the following figure and scale it by 2, It’s new dimensions are 4 cm by 10 cm, by 20 cm

  16. Homework Page 16-17, #6, 7 Page 18, #11A-C Page 22, #24 Page 59, #8-10 Page 60, #11 Page 61, #18-20, 22, 23

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