#### Transcript of 12.3: Surface Area of Pyramids and Cones

**12.3: Surface Area of Pyramids and Cones**

Terms You Need to Know:

Regular Pyramid:

A pyramid that has a base which is a regular polygon and the altitude has an endpoint on the center of the base. The faces are also isosceles triangles.

Slant Height:

Height of each lateral face

Right Cone:

A cone where the axis is also the altitude

Oblique Cone:

A cone where the axis is not the altitude

*AXIS IS THE LINE FROM THE VERTEX TO THE CENTER*

Surface Area of Regular Pyramids

The formula for finding a regular pyramid's surface area is:

SA=0.5PL+B

Surface/Lateral Area of Cones

The formulas for finding the lateral and surface area of cones are:

Lateral Area of Regular Pyramids

The formula for finding lateral area of regular pyramids is:

LA=0.5PL

Pyramids

Cones

Where

P

is the perimeter of the base,

L

is the slant height, and

B

is the area of the base

Where

P

is the perimeter of the base and

L

is the lateral or slant height

*Remember that you can find the slant(lateral) height a pyramid or cone by using the Pythagorean Theorem*

JUST TO RECAP...

Questions:#1

Find the slant height of a pyramid if the surface area is 64 uts.^2 and the base is a square with a side 7 uts. long

Answer

64=0.5(28x)+7^2

64=14x+49

15=14x

x=15/14

Therefore the slant height is 15/14 units

Questions:#2

Find the surface area of a cone with a radius of 7.5 cm. and a slant height of 44 cm

Answer

r^2

+

rl

7.5^2pi+44(7.5)pi

56.25pi+330pi

386.25pi

1213 uts. (rounded to nearest whole #)

Questions:#3

Find the lateral area of a cone if the radius is X inches, with the net plane of the face being an equilateral triangle and the axis is 40 inches. (Round to the nearest tenth)

Make your triangle

30-60-90

Because of the triangle, you have the radius which is (40 square root 3)/3 and the slant height is (80 root 3)/3

pi(rl) is the formula

(40 root 3)(80 root 3)pi/9

10048/3

3349.3 in.^2

Answer

Questions:#4

Find the lateral area of a pyramid with equilateral faces in Egypt with the base being a square with an edge of 8 inches, and a slant height of 30 inches.

(1 in. =500 ft.)

Answer

[(8*4)(30)]/2=A

960/2=A

480 in=A

(500)(500)(480)=A

120000000 ft. squared

A Little More Reasoning

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