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12.2 Surface Area of Prisms and Cylinders

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This document discusses calculating the surface area of prisms and cylinders. It provides formulas for finding the lateral area and total surface area of prisms and cylinders. For prisms, the lateral area is calculated as the perimeter times the height, and the total surface area adds the lateral area and twice the area of the bases. For cylinders, the lateral area uses the circumference times the height, and the total surface area adds the lateral area and twice the area of the circular bases. Examples are provided to demonstrate calculating the lateral and total surface areas of specific prisms and cylinders.

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Prisms and Cylinders The student is able to (I can): Calculate the surface area of prisms and cylinders
The surface area is the total area of all faces and curved surfaces of a three-dimensional figure. The lateral area of a prism is the sum of the areas of the lateral faces. Lets look at a net for a hexagonal prism:
The surface area is the total area of all faces and curved surfaces of a three-dimensional figure. The lateral area of a prism is the sum of the areas of the lateral faces. Lets look at a net for a hexagonal prism: What shape do the lateral faces make? (a rectangle)
If each side of the hexagon is 1 in., what is the perimeter of the hexagon? What is the length of the base of the big rectangle? 6 in. 6 in.
This relationship leads to the formula for the lateral area of a prism: L = Ph where P is the perimeter and h is the height of the prism. For the total surface area, add the areas of the two bases: S = L + 2B
A net of a cylinder looks like: The length of the lateral surface is the circumference of the circle, so the formula changes to: L = Ch where C = d or 2r and the formula for the total area is now: S = L + 2r2
Examples: Find the lateral and total surface area of each. 1. 2. 10 cm 14 cm 4" 3" 8" 5"
Examples: Find the lateral and total surface area of each. 1. 2. 10 cm 14 cm 4" 3" 8" 5" P = 3+4+5 = 12 in. B = 遜(3)(4) = 6 in2 L = (12)(8) = 96 in2 S = 96 + 2(6) = 108 in2 C = 10 cm B = 52 = 25 cm2 L = (10)(14) = 140 cm2 S = 140 + 2(25) = 190 cm2

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12.2 Surface Area of Prisms and Cylinders

  • 1. Prisms and Cylinders The student is able to (I can): Calculate the surface area of prisms and cylinders
  • 2. The surface area is the total area of all faces and curved surfaces of a three-dimensional figure. The lateral area of a prism is the sum of the areas of the lateral faces. Lets look at a net for a hexagonal prism:
  • 3. The surface area is the total area of all faces and curved surfaces of a three-dimensional figure. The lateral area of a prism is the sum of the areas of the lateral faces. Lets look at a net for a hexagonal prism: What shape do the lateral faces make? (a rectangle)
  • 4. If each side of the hexagon is 1 in., what is the perimeter of the hexagon? What is the length of the base of the big rectangle? 6 in. 6 in.
  • 5. This relationship leads to the formula for the lateral area of a prism: L = Ph where P is the perimeter and h is the height of the prism. For the total surface area, add the areas of the two bases: S = L + 2B
  • 6. A net of a cylinder looks like: The length of the lateral surface is the circumference of the circle, so the formula changes to: L = Ch where C = d or 2r and the formula for the total area is now: S = L + 2r2
  • 7. Examples: Find the lateral and total surface area of each. 1. 2. 10 cm 14 cm 4" 3" 8" 5"
  • 8. Examples: Find the lateral and total surface area of each. 1. 2. 10 cm 14 cm 4" 3" 8" 5" P = 3+4+5 = 12 in. B = 遜(3)(4) = 6 in2 L = (12)(8) = 96 in2 S = 96 + 2(6) = 108 in2 C = 10 cm B = 52 = 25 cm2 L = (10)(14) = 140 cm2 S = 140 + 2(25) = 190 cm2