surface area of solids
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SURFACE AREA OF SOLIDS
March 22, 2010
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Three-Dimensional Figures
Prism – a 3D solid with two parallel, congruent faces called bases
Pyramid – a 3D solid with one base that is any polygon; the other faces are triangles
Cylinder – a 3D solid that has two parallel, congruent circular bases connected with a curved side
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Surface Area
Surface area refers to the sum of the areas of all the surfaces of a 3D figure.
Also called Total Surface Area (TSA) Examples:
wrapping paper orange
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Lateral Surface Area
Lateral surface area of a solid only includes the faces or surfaces that make up the sides of the solid (not the base(s))
Examples: Soup can label
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With a partner, you will determine the surface area of various geometric solids.
How Do You Find the Surface Area of a Solid?
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4*s2 where s = length of side
6*s2
4*s*h, where s=length of side of base, h = height(2*s2)+(4*s*h)
3*s*h, where s=length of side of base, h = height of prism
3/2*s*l, where s=length of side of base, l=slant height
(3*s*h)+(s*a) where a=altitude of triangle
(1/2*s*a)+(3/2*s*l) where a =altitude of triangle at base2*s*l, where s=length of side of base, l=slant heights2 + (2*s*l)
2*π*r*h, where r = radius, h = height(2*π*r2)+(2*π*r*h)
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Practice
Both containers hold about the same amount of pineapple juice. Does the box or the can have a greater surface area?
6 cm
9 cm9 cm
5 cm
5 cm
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Practice
6 cm
9 cm
Surface Area of can
rhrS 22 2 )9)(3(2)3(2 2 S
5418 S272 cmS 22.226 cmS
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Practice
Surface Area of box
)4()2( 2 shsS ))9)(5(4()5*2( 2 S
18050S2230 cmS
9 cm
5 cm
5 cm
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Practice
Since 230cm2 > 288.2cm2, the box has a greater surface area.
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Practice – Architecture
The Louvre museum in Paris has a huge square glass pyramid at the entrance with a slant height of about 92 feet. Its square base is 116 feet on each side. How much glass did it take to cover the pyramid?
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Practice
92 feet
116 feet
Find the lateral area only since the bottom of the pyramid is not covered in glass.
slLSA 2)92)(116(2LSA2344,21 ftLSA