Transcript Chapter 12 Notes: Surface Area and Volume of Prisms

Chapter 12 Notes: Surface
Area and Volume of Prisms
Goal: Students will find the surface area and
volume of prisms.
• 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.
• 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.
• 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.
Ex.1: Find (a) the lateral area, and (b) the surface
area of the prism.
3 cm
4 cm
6 cm
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.
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.
• 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.
• Find the volume of the solid.
Ex.5:
Ex.6:
10 cm
20 cm
24 cm
Ex.7:
10 in
8 in
8 in
8 in
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.
Ex.9: The volume of the cube is 90 cubic inches. Find
the value of x.
Ex.10: Find the volume of the right hexagonal prism.
Ex.11: Find the volume of the puzzle piece in cubic
units.
Ex.12: Find the surface area of the solid formed by the
net. Round your answer to two decimal places.