Find the Surface Area…

Find the surface area of a cylinder with a

diameter of 10cm and a height of 15cm.

S.A. = 2r2 + 2rh = 2(5)2 + 2(5)(15)

S.A. = 200

Surface Areas of

Pyramids

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Pyramids

Pyramid

Pyramid – A three dimensional figure in

which one face, the base, is any polygon

and the lateral faces are triangles that

meet at a common vertex.

vertex

Pyramids cont.

The altitude of a pyramid is the

perpendicular segment from the vertex to

the plane of the base.

The length of the altitude is called the

height. Height

h

Pyramid

Pyramids cont.

Regular Pyramid – a pyramid whose base

is a regular polygon.

Slant Height – the length of the altitude of

the lateral face.

Slant

Height

Pyramid

Formulas

Lateral Area and Surface Area of a Regular Pyramid

PL2

1

Lateral

Area Base

Perimeter Slant

Height

ALS

Surface

Area Lateral

Area

Base Area

B

Example 1: Finding Surface Area

of a Pyramid

Find the surface area of a square pyramid with base edges 5 m and slant height 3 m.

m 3

m 5

ALS

PL2

1

Questions Answers B Square

F L x w

A

What is the SLANT

HEIGHT?

What is the perimeter of

the base?

L

S = L + A

#2 Finding Surface Area of a

Pyramid

Find the surface area of a regular hexagonal pyramid with a slant height 20 in and sides 8 in.

ALS

pL2

1

in 8

in 02

in 34

Questions Answers B Square

F L x w

A

What is the SLANT

HEIGHT?

What is the perimeter of

the base?

L

S = L + A

#3 Find the surface area of:

12 m

pL2

1

Questions Answers B Square

F L x w

A

What is the SLANT

HEIGHT?

What is the perimeter of

the base?

L

S = L + A

#4 Find the surface area of:

10”

15”

10”

Questions Answers B Square

F L x w

A

What is the SLANT

HEIGHT?

What is the perimeter of

the base?

L

S = L + A

pL2

1

Surface of a Cone

Finding the Base is Easier, since it is a circle.

rrAS 2..

Surface of a Cone

Finding the Surface Area.

r = 5, h = 12

rrAS 2..

Questions Answers r

What is the SLANT

HEIGHT?

Surface of a Cone

Finding the Surface Area.

r = 5, h = 12; need l

rrAS 2..

Surface of a Cone

Finding the Surface Area.

r = 5, h = 12; need l

rrAS 2..

13169

14425

125

2

222

Surface of a Cone

Finding the Surface Area.

r = 5, h = 12; need l

rrAS 2..

90..

6525..

1355.. 2

AS

AS

AS