Surface Area of Composite Shapes

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Show your work for each problem.

1.
When two cubes are joined face-to-face, how many faces become hidden?
1. a)6 faces
2. b)2 faces
3. c)4 faces
4. d)1 face
2.
A cone sits on top of a cylinder (same radius). Which formula should you use for the cone's surface area?
1. a)Curved surface area only:
2. b)Total surface area:
3. c)Just the base:
4. d)Double the curved surface:
3.
A cube has a surface area of . If a cylindrical hole is drilled through it, removing of surface but exposing of inner surface, what is the new total surface area?
4.
What happens to the total surface area when a hemisphere is placed on top of a cylinder (same radius)?
1. a)Double everything
2. b)Add hemisphere curved surface, subtract the hidden circle
3. c)Just use the hemisphere surface area
4. d)Add hemisphere surface area + cylinder surface area
5.
Two cubes, each with side length , are joined face-to-face. What is the total surface area of the composite shape in ?
6.
A cylinder (radius , height ) has a cone (same radius, slant height ) on top. Find the total exterior surface area. Use .
7.
A cube with side has a cube with side placed on top of it (centered). What is the total surface area in ?
8.
A cube with side has a cylindrical hole (radius ) drilled completely through. Find the total surface area. Use .
9.
A rectangular prism () has a smaller rectangular prism () attached on top. How many square units of surface are hidden?
1. a) square units
2. b) square units
3. c) square units
4. d) square units
10.
A building has a rectangular base () with a hemispherical dome (radius ) on the roof. Calculate the total exterior surface area (excluding the floor). Use .
11.
A cylinder (radius , height ) has a hemisphere (radius ) on top and a cone (radius , slant height ) on bottom. What is the total surface area? Use .
12.
A house has walls that form a rectangular prism (). The roof is a triangular prism with the triangle having base and height . The slant height of the roof is . Find the total exterior surface area (no floor).
13.
A sphere (radius ) has a cylindrical hole (radius , depth ) drilled into it (not through). The hole exposes the cylinder's curved surface inside. What is the total surface area? Use .
14.
Three identical cubes (side ) are joined in a row. What is the total surface area of the composite shape?
1. a)
2. b)
3. c)
4. d)
15.
Which statement about composite shape surface area is TRUE?
1. a)Always add all component surface areas together
2. b)Components never share faces
3. c)Holes reduce total surface area
4. d)Hidden faces must be subtracted from the total