12.2 Surface Area of Prisms & Cylinders · 2017-10-18 · Surface area of cylinders •The lateral area of a cylinder is the area of its curved surface. The lateral area is equal

12.2 Surface Area

of Prisms &

Cylinders Geometry

Mr. Peebles

Spring 2013

Please get your whiteboards,

markers, and towels then have a

seat and wait for instructions.

Geometry Bell Ringer

Geometry Bell Ringer

Answer: B

Daily Learning Target

(DLT) • “I can understand, apply, and

remember to find the surface area of

prisms and cylinders.”

Assignment Pages 601-604

(1-9, 13-15, 24-26, 30, 55-58)

Assignment Pages 601-604

(1-9, 13-15, 24-26, 30, 55-58)

1. Vertices: 4 4. Faces = 8 Edges: 6 5. Edges = 12

Faces: 4 6. Edges = 12

2. Vertices: 8 7. Vertices = 8 Edges: 12 8. Vertices = 5

Faces: 6 9. Vertices = 9

3. Vertices: 10 13. Two Edges: 15 Concentric

Faces: 7 Circles

Assignment Pages 601-604

(1-9, 13-15, 24-26, 30, 55-58) 14.Triangle

15.Rectangle

24.Triangle

25.Circle

26.Trapezoid

30.Vertices = 60

55.B

56.G

57.D

58.J

Finding the surface area of a

prism

• 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.

Finding the surface area of a

prism

• The altitude or height of

a prism is the

perpendicular distance

between its bases. In a

right prism, each lateral

edge is perpendicular to

both bases. Prisms that

have lateral edges that

are not perpendicular to

the bases are oblique

prisms. The length of

the oblique lateral edges

is the slant height of the

prism.

Note

• Prisms are classified by the shape of

their bases. For example, the figures

above show one rectangular prism

and one triangular prism. The surface

area of a polyhedron is the sum of the

areas of its faces. The lateral area of

a polyhedron is the sum of the areas

of its lateral faces.

Ex. 1: Finding the surface

area of a prism

• Find the surface

area of a right

rectangular prism

with a height of 8

inches, a length of

3 inches, and a

width of 5 inches.

Ex. 2: Finding the surface

area of a prism

• Find the surface

area of a box of

cereal with a height

of 15 inches, a

length of 8 inches,

and a width of 4

inches.

Ex. 2: Finding the surface

area of a prism

• Find the surface area of a box of

cereal with a height of 15 inches, a

length of 8 inches, and a width of 4

inches.

Faces Dimensions Area of Faces

Left & Right 15” x 8” 120 in2

Front & Back 15” x 4” 60in2

Top & Bottom 8” x 4” 32in2

SA = 2(120) + 2(60) + 2(32) = 424 in2

Nets • Imagine that you cut some edges of a

right hexagonal prism and unfolded it.

The two-dimensional representation of

all of the faces is called a NET.

Ex. 2: Using Theorem 12.2

Ex. 2: Using Theorem 12.2

Ex. 2: Using Theorem 12.2

Finding the surface area of a cylinder

• A cylinder is a solid with congruent circular bases that lie in parallel planes. The altitude, or height of a cylinder is the perpendicular distance between its bases. The radius of the base is also called the radius of the cylinder. A cylinder is called a right cylinder if the segment joining the centers of the bases is perpendicular to the bases.

Surface area of cylinders

• The lateral area of a cylinder is the area of its

curved surface. The lateral area is equal to the

product of the circumference and the height,

which is 2rh. The entire surface area of a

cylinder is equal to the sum of the lateral area

and the areas of the two bases.

Ex. 3: Finding the Surface Area of a Cylinder

Find the surface area of the right cylinder.

Ex. 3: Finding the Surface Area of a Cylinder

Find the surface area of the right cylinder.

Ex. 4: Finding the height of a cylinder

• Find the height of a cylinder which

has a radius of 6.5 centimeters

and a surface area of 592.19

square centimeters.

Ex. 4: Finding the height of a cylinder

• Find the height of a cylinder which

has a radius of 6.5 centimeters

and a surface area of 592.19

square centimeters.

Assignment Pages 611-614 (1, 2, 5, 6, 8, 9, 11, 13, 22,

23, 38-40)

Exit Quiz – 4 Points

Mario’s company makes unusually

shaped imitation gemstones. One

gemstone had 10 faces and 12 vertices.

How many edges did the gemstone

have?

a. 20 edges b. 23 edges

c. 25 edges d. 22 edges

Formula: F + V = E + 2