prisms. a prism has two parallel faces, called bases, that are congruent polygons. the lateral faces...
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Prisms
PrismsA prism has two parallel faces, called bases, that are congruent polygons.The lateral faces are rectangles in a right prism, or parallelograms in an oblique prism.
Lateral faces
Page 1
Volume of a Prism
BhV Volume equals BIG B times h!
B = Area of the baseh = the height of the prism
Page 1
Rectangular PrismsA rectangular prism has rectangular bases and lateral edges perpendicularto the bases.
Lets find the volume and surfacearea of the prism shown!
Page 2
π= hπ΅π=(ππ€)h
πππππ π΅=ππ€
π=(7)(5)(4)π=140
π= hππ€Useful Formula: Volume of a Rectangular Prism!
Examples Page 3
π΄π΅πΆπ·β πΈπΉπΊπ»
π΄πΈπ»π·β π΅πΉπΊπΆ
π΄π΅πΉπΈβ πΆπΊπ»π·
Page 4
π= hπ΅ Since B = a triangle, use the area formula for a triangle.
π=(12ππ€)h
π=12
(10 ) (10 ) (3 )
π=150βππ β
πΉπππ π΅ ππππ π‘ , hπ‘ πππ π’π πππ΅=
12hπ
π΅=12(10)(10 )
π΅=50
π= hπ΅π=(50)(3)π=150
Page 4
π= hπ΅Since B = a rectangle, use the area formula for a rectangle.
π= hππ€
π=3 π β3π€ β3hπ=27 β hππ€
π‘πππππ hπ‘ π hπππππ‘ =ΒΏ3 ππ‘πππππ hπ‘ π hπ€πππ‘ =ΒΏ3π€π‘πππππ hπ‘ πh hπππ π‘=ΒΏ3h
ππΈπ πππΏπππΈ :
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π=π3
π=83
π=512
Page 4
π= hπ΅π= (48 ) (6 )π=288
π=48h288=48h288=48h6=h
ππππ’ππ hπ πππ΅ππ₯ ππππ’πππππ .ππππ π
Page 4
π= hπ΅ Since B = a triangle, use the area formula for a triangle.
π=(12ππ€)h
48=12
(8 ) (8 )h
48=32h1 .5=h
Page 4
π= hπ΅Since B = a rectangle, use the area formula for a rectangle.
π= hππ€π= (π‘+2 ) (π‘ ) (3 π‘ )π= (π‘+2 ) (3 π‘ 2 )π=3π‘ 3+6 π‘ 2
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Page 5
π= hπ΅Since B = a rectangle, use the area formula for a rectangle.
π= hππ€
πππ€ππππ’ππ :π=2 π β2π€ β4 hπ=16 hππ€
πππ’πππ hπ‘ π hπππππ‘ =ΒΏ2 ππππ’πππ hπ‘ π hπ€πππ‘ =ΒΏ2π€ππ’ππππ’πππ hπ‘ πh hπππ π‘=ΒΏ4h
Page 5
π= hπ΅Since B = a rectangle, use the area formula for a rectangle.
π= hππ€π= (6 ) (3 ) (4 )π=72
Page 6
π= hπ΅Since B = a rectangle, use the area formula for a rectangle.
π= hππ€π= (4 ) (6 ) (12 )π=288
Page 6
π=π3
8=π33β8=3βπ32=π
π=π3
216=π33β216=3βπ36=π
Page 6
π= hπ΅42=π΅ β314=π΅
Page 6
π= hπ΅Since B = a rhombus, use the area formula for a rhombus that utilizes the diagonals.
π=12π1 βπ2 β h
π=12
(12 ) (16 ) (20 )
π=1920
π΅ ( hπ ππππ’π )=12π1βπ2
Page 6
2472
8 β6480=51840
π= hπ΅
Since B = a rectangle, use the area formula for a rectangle.
π= hππ€51840=(72 ) (24 )h51840=1728h30=h
Minimum height is 30 inches
Homework
β’Page 6#2,4,5c,d,e,7,9,19
Page 6
π=π3
π=253
π=15625
Page 6
π= hπ΅Since B = a square, use the area formula for a square.
π=π 2h
π=72β3π=147
Page 6
π=π3
64=π33β64= 3βπ34=π
π=π3
125=π33β125=3βπ35=π
π=π3
27=π33β27=3βπ33=π
Page 6
π= hπ΅9=18h918
=1818h
12=h
Page 6
π= hπ΅Since B = a rhombus, use the area formula for a rhombus that utilizes the diagonals.
π=12π1 βπ2 β h
60=12
(10 β12 )h
60=60h1=h
Page 6
π= hπ΅ π=10 hπ΅The volume would be 10 times the original volume.