chapter 12 notes: surface area and volume of prisms goal: students will find the surface area and...
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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.