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12.3: Surface Area of Pyramids and Cones
Transcript of 12.3: Surface Area of Pyramids and Cones
Terms You Need to Know:
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.
Height of each lateral face
A cone where the axis is also the altitude
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:
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:
is the perimeter of the base,
is the slant height, and
is the area of the base
is the perimeter of the base and
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...
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
Therefore the slant height is 15/14 units
Find the surface area of a cone with a radius of 7.5 cm. and a slant height of 44 cm
1213 uts. (rounded to nearest whole #)
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
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
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.)
120000000 ft. squared
A Little More Reasoning