11.2 Surface Areas of Prisms and Cylinders

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11.2 Surface Areas of Prisms and Cylinders

• A prism is a polyhedron with two congruent,
  parallel faces, called bases.
• The other faces are lateral faces.
• You name prisms based on using the shapes of the
  bases.

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Prisms

• An altitude of a prism is a perpendicular segment
  that joins the planes of the bases.
• The height, h, of a prism is the length of an
  altitude.
• A prism may either be right or oblique.
• Right prism the lateral faces are rectangles
  and a lateral edge is an altitude.
• Oblique prism some or all of the lateral faces
  are nonrectangular.

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Prisms

• Lateral Area (L.A.) of a prism is the sum of the
  areas of the lateral faces.
• Surface Area (S.A.) of a prism is the sum of the
  lateral area and the area of the two bases.

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Find the Surface Area of a Prism

• What is the surface area of the prism?

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Lateral and Surface Areas of a Prism

• The lateral area of a right prism is the product
  of the perimeter of the base and the height of
  the prism.
• L.A. Ph
• The surface area of a right prism is the sum of
  the lateral area and the areas of the two bases.
• S.A. L.A. 2B

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Using Formulas to Find Surface Area of a Prism

• What is the surface area of the prism?

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Cylinders

• A cylinder is a solid that has two congruent
  parallel bases that are circles.
• An altitude of a cylinder is a perpendicular
  segment that joins the planes of the bases.
• The height, h, of a cylinder is the length of an
  altitude.
• In a right cylinder, the segment joining the
  centers of the bases is an altitude.
• In an oblique cylinder, the segment joining the
  centers is not perpendicular to the planes
  containing the bases.

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Lateral and Surface Areas of a Cylinder

• The lateral area of a right cylinder is the
  product of the circumference of the base and the
  height of the cylinder.
• L.A. 2prh or L.A. pdh
• The surface area of a right cylinder is the sum
  of the lateral area and the areas of the two
  bases.
• S.A. L.A. 2B or S.A. 2prh 2pr²

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Finding Surface Area of a Cylinder

• The radius of the base of a cylinder is 4 in. and
  its height is 6 in. What is the surface area of
  the cylinder in terms of p?

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Finding Lateral Area of a Cylinder

• You are using a cylindrical stencil roller to
  paint patterns on your floor. What area does the
  roller cover in one full turn if it has a
  diameter of 2.5 in. and a height of 6 in.?

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More Practice!!!!!

• Homework Textbook p. 703 704 1 20 ALL.