Chapter 12 Notes: Surface Area and Volume of Prisms

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Chapter 12 Notes Surface Area and Volume of
Prisms

• Goal Students will find the surface area and
  volume of prisms.

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• A prism is a polyhedron with two congruent faces,
  called bases, that lie in parallel planes.
• The other faces, called lateral faces, are
  parallelograms formed by connecting the
  corresponding vertices of the bases.
• The segments connecting these vertices are
  lateral edges.
• Prisms are classified by the shapes of their
  bases.

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• Right Prisms
• The height of a prism is the perpendicular
  distance between its bases, called an altitude.
• A prism may be either right or oblique.
• In a right prism, each lateral edge is
  perpendicular to both bases.
• A prism with lateral edges that are not
  perpendicular to the bases is an oblique prism.

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• Theorem 12.2 Surface Area of a Right Prism
• The lateral area of a prism is the sum of the
  areas of the lateral faces.
• The surface area of a prism is the sum of the
  areas of the lateral faces and the two bases.
• Lateral Area L.A ph
• Surface Area S ph 2B
• where P is the perimeter of the base, h is the
  height of the prism, and B is the area of the
  base.

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• Ex.1 Find (a) the lateral area, and (b) the
  surface area of the prism.
• 3 cm
  4 cm
• 
  6 cm

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• Ex.2 Find the lateral area and surface area of a
  right rectangular prism with height 7 inches,
  length 3 inches, and width 4 inches.
• Ex.3 Find the surface area of the right
  pentagonal prism.

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• Volume of Prisms
• Postulate 27 Volume of a Cube
• V s3
• where s is the length of the base edge.
• Ex.4 Find the volume of a cube that has a side
  length of 6 cm.

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• Theorem 12.6 Volume of a Prism
• Volume V Bh
• where B is the area of the base, and h is the
  height of the prism.

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• Find the volume of the solid.
• Ex.5

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• Ex.6
• 
  10 cm
• 
  
• 
  20 cm
• 24 cm

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• Ex.7
• 10 in
• 8 in
• 
  8 in
• 8 in

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• Ex.8 The volume of a triangular prism is 1860
  cm3. Its base is a right triangle with legs 24 cm
  and 10 cm long.
• a. Draw and label a diagram.
• b. Find the area of the base of the prism.
• c. Find the height of the prism.

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• Ex.9 The volume of the cube is 90 cubic inches.
  Find the value of x.

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• Ex.10 Find the volume of the right hexagonal
  prism.

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• Ex.11 Find the volume of the puzzle piece in
  cubic units.

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• Ex.12 Find the surface area of the solid formed
  by the net. Round your answer to two decimal
  places.