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12.3: Surface Area of Pyramids and Cones

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derp gat

on 19 May 2015

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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
Full transcript