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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