Surface area of prisms and cylinders
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Surface Area of Prisms and Cylinders. Lesson 9-8. Vocabulary. A net is a pattern you can fold to form a three-dimensional figure. This is a net for a triangular prism. The surface area of a three-dimensional figure is the sum of the areas of its surfaces.

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Surface Area of Prisms and Cylinders

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Surface area of prisms and cylinders

Surface Area of Prisms and Cylinders

Lesson 9-8


Vocabulary

Vocabulary

  • A net is a pattern you can fold to form a three-dimensional figure.

This is a net for a triangular prism.


Surface area of prisms and cylinders

  • The surface area of a three-dimensional figure is the sum of the areas of its surfaces.

  • Find the area of each surface, and add all the areas together.


Example 1

Example 1

Triangles

A = ½ bh

A = ½ (26)(18)

8 cm

A = ½ (468)

18 cm

A = 234 cm2

26 cm

2 Tri’s: 234 x 2 = 468 cm2

Left Rectangle

Front and Back Rectangles

A = lw

A = lw

A = (26)(8)

A = (18)(8)

A = 208 cm2

A = 144 cm2

2 Rect’s: 208 x 2 = 416 cm2


Add up the areas to find surface area

Add up the areas to find surface area.

S.A. = 468 cm2 + 144 cm2 + 416 cm2

S.A. = 1,028 cm2


Surface area of a cube

Surface Area of a Cube

  • A cube has 6 congruent square faces.

  • Find the area of one face, and multiply it by 6.


Example

Example

A = s2

A = 72

A = 49 in2

7 in

S.A. = 49(6)

S.A. = 294 in2


Surface area of a cylinder

Surface Area of a Cylinder

  • A cylinder consists of two circle bases and one rectangular side.

  • The length of the rectangle is equal to the circumference of the circle.

  • Find the area of the circles and add it to the area of the rectangle.


Example1

Example

Rectangle

5 m

The width of the rectangle is the height of the cylinder (16 m). The length of the rectangle is the circumference of the circle.

16 m

Area of the circles

C = 2r

C = 2(3.14)(5)

A = r2

C = 31.4 m

A = 3.14(52)

A = lw

A = 3.14 (25)

A = 31.4(16)

A = 78.5 m2

A = 502.4 m2

2 circles: 78.5 x 2 = 157 m2


Put the areas together

Put the areas together:

S.A. = 157 m2 + 502.4 m2

S.A. = 659.4 m2


Homework time

Homework Time


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