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12.3 Surface Area of Pyramids and Cones Geometry Mr. Peebles Spring 2013
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### Transcript of 12.3 Surface Area of Pyramids and Cones - Montgomery …€¦ ·  · 2017-10-18•Find the surface...

12.3 Surface Area of

Pyramids and Cones

Geometry

Mr. Peebles

Spring 2013

Geometry Bell Ringer-Whiteboard,

• Find the surface area of the cylinder in

terms of pi with a radius of 8 in and a

height of 11 in.

• a. 688p in.2 b. 304p in.2

c. 176p in.2 d. 208p in.2

Formula: SA = 2πr2 + 2πrh

Geometry Bell Ringer

• Find the surface area of the cylinder in

terms of pi with a radius of 8 in and a

height of 11 in.

• a. 688p in.2 b. 304p in.2

c. 176p in.2 d. 208p in.2

Daily Learning Target (DLT)

Monday January 28, 2013 • “I can understand, apply, and remember

to find the surface area of a pyramid

and cone.”

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

23, 38-40)

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

23, 38-40)

1. 1726 cm2 13. 107 in2

2. 216 ft2 22. C

5. Lateral Area: 120 ft2 23. 47.5 in2

Surface Area: 220 ft2 38. C

6. Lateral Area: 96 in2 39. J

Surface Area: 108 in2 40. D

8. 40π cm2

9. 16.5π cm2

11. 36.8 cm2

Finding the surface area of a

pyramid • A pyramid is a polyhedron in which the base

is a polygon and the lateral faces are triangles with a common vertex. The intersection of two lateral faces is a lateral edge. The intersection of the base and a lateral face is a base edge. The altitude or height of a pyramid is the perpendicular distance between the base and the vertex.

More on pyramids

• A regular pyramid has a

regular polygon for a

base and its height

meets the base at its

center. The slant height

of a regular pyramid is

the altitude of any

lateral face. A

nonregular pyramid

does not have a slant

height.

Lateral & Surface Area of A

Regular Pyramid

LA = ½ pl

p = Perimeter of Base

l = Slant Height of Pyramid

SA = LA + B

LA = Lateral Area of Pyramid

B = Area of Base

Pyramid Arena

Ex. 1: Finding the Area of a

Lateral Face

• Architecture. The lateral faces of the

Pyramid Arena in Memphis, Tennessee,

are covered with steel panels. Use the

diagram of the arena to find the area of

each lateral face of this regular pyramid.

Ex. 2: Finding the surface area

of a pyramid

• To find the surface area

of the regular pyramid

shown, start by finding

the area of the base.

• Use the formula for the

area of a regular

polygon,

½ (apothem)(perimeter).

A diagram of the base

is shown to the right.

Ex. 2: Finding the surface area

of a pyramid

After substituting, the

area of the base is

½ (3 )(6• 6), or

54 square meters.

3

3

Surface area

• Now you can find the surface area by

using 54 for the area of the base, B. 3

Questions?

Finding the Surface Area of a Cone

• A circular cone, or cone, has a circular base and a vertex that is NOT in the same plane as the base. The altitude, or height, is the perpendicular distance between the vertex and the base. In a right cone, the height meets the base at its center and the slant height is the distance between the vertex and a point on the base edge.

Finding the Surface Area of a Cone

• The lateral surface of a

cone consists of all

segments that connect the

vertex with points on the

base edge. When you cut

along the slant height and

like the cone flat, you get

the net shown at the right.

In the net, the circular base

has an area of r2 and the

lateral surface area is the

sector of a circle.

Theorem

• Surface Area of a Right

Cone

The surface area S of a right cone is S = r2 + rl,

where r is the radius of the base and l is the slant

height

Ex. 3: Finding the surface area

of a cone

• To find the surface area

of the right cone shown,

use the formula for the

surface area.

S = r2 + rl Write formula

S = 42 + (4)(6) Substitute

Ex. 3: Finding the surface area

of a cone

• To find the surface area

of the right cone shown,

use the formula for the

surface area.

S = r2 + rl Write formula

S = 42 + (4)(6) Substitute

S = 16 + 24 Simplify

S = 40 Simplify

The surface area is 40 square inches or about

125.7 square inches.

Questions?

Assignment Pages 620-623 (1-13 Odds, 23, 27, 28-30,

46-48)

Closure - Whiteboards Find the surface area of a cone with a radius

of 10 FT and a slant height of 15 FT and please leave your answer in terms of pi.

Exit Quiz – 5 Points

Find the surface area of the right cylinder.

Leave your answer in terms of pi