Derive Formulas of Surface Area – Right Prisms and Right Cylinders.
Transcript of Derive Formulas of Surface Area – Right Prisms and Right Cylinders.
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Derive Formulas of Surface Area – Right Prisms and Right
Cylinders
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Definition of a Prism
A Prism is a solid having bases or ends that are parallel, congruent polygons and sides that are parallelograms.
http://dictionary.reference.com/browse/prism
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Parts of a Right PrismThe bases are congruent and parallel
The lateral faces are the faces connecting the corresponding vertices of the bases
Lateral edges are the segments connecting the lateral faces
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Different Right Prisms
All Prisms with a Right angle
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Oblique PrismA prism that has lateral edges that are not
perpendicular to the bases.
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Height vs. Slant Height
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A way to show the surface of a Prism
A two Dimensional representation of a prism is called a net
H
W
H
L
W
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Another way is adding all the faces and bases
The equation
S.A. = 2(W·H + W·L + H·L)
W = 4; L = 7; H = 5
166832..
3528202..
7574542..
AS
AS
AS
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To find surface area of a rectangular prism
S.A. = 2(2 x 4) + 2(3 x 4) + 2(2 x 3)
S.A. = 2(8) + 2(12) + 2(6)
S.A. = 16+ 24+ 12
S.A. = 52
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Let’s Derive Surface Area Prism
SA = 2lw + 2wh + 2lhSA = 2lw + h(2w + 2l)SA = 2 bases + h perimeter⋅
HPBAS 2..
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Surface Area of a Right Prism Theorem 12.2
The Surface Area of a Prism is the sum of two base areas and the lateral face areas.
Lateral faces = Height times Perimeter
B is area of a base
P is perimeter of the base
H is height
HPBAS 2..
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Right Prism Theorem
The Base is 4(7)= 28
Perimeter is 2(4)+2(7) = 22
Height is 5
S.A. = 2(28) + 22(5)
S.A. = 166
HPBAS 2..
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Your Turn!!!• Find the surface area
The bases are 12x2
S.A. = 2B+PhS.A. = 2(12x2) + 28x7S.A. = 48+196S.A. =244 cm2
Perimeter = 24 + 4H= 7
The bases are (11x17)/2
Perimeter = 11 +17 +20H = 6
S.A. = 2B+PhS.A. = 2(11x17)/2+ 48x6S.A. = 187+ 288S.A. =475 cm2
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Define of a Cylinder
A Prism with a circular base
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The net of a Cylinder
Two circles and a Rectangle
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The Surface Area of a Cylinder
2 Bases + Circumference times height
HCBAS 2..
12
42
4 2
H
C
Base
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The Surface Area of a Cylinder2 Bases + Circumference times height
HCBAS 2..
12
42
4 2
H
C
Base
128..
9632..
128162..
AS
AS
AS
hrrAS 22.. 2