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Surface Area. Slideshow 49, Mathematics Mr Richard Sasaki Room 307. Objectives. Review how to find the area of various polygons Learn how to calculate the surface area of cuboids, triangular prisms and square-based pyramids Learn how to calculate the surface area of a cylinder. Answers. - PowerPoint PPT Presentation
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Surface Area
Slideshow 49, MathematicsMr Richard Sasaki
Room 307
Objectivesβ’ Review how to find the area of
various polygonsβ’ Learn how to calculate the
surface area of cuboids, triangular prisms and square-based pyramids
β’ Learn how to calculate the surface area of a cylinder
Answers15ππ2 49ππ2 8ππ2
108ππ2 91ππ2 70ππ2
26ππ2 135ππ2 204 ππ2
Surface AreaWhat is surface area?The total area of faces & surfaces on a 3D shape.Calculating surface area for cuboids and triangular prisms is easy as long as we know the dimensions of each face.
5ππ 2ππ3ππ
5ππ 2ππ3ππ2ππ3ππ
Surface Area - Cuboid
5ππ 2ππ3ππ
5ππ 2ππ3ππ2ππ
3ππ
All we do is add the total area of each face.
10ππ215ππ210ππ26ππ2 6ππ215ππ2
We just simply add the numbers together.10+15+10+15+6+6ΒΏ20+30+12
ΒΏ62ππ2
Triangular PrismVisualising a net is always good!
4ππ10ππ
5ππ
3ππ
10ππ4ππ3ππ5ππ3ππ
4ππ
Surface Area: (10 β4 )+ΒΏ(10 β3 )+ΒΏ(10 β5 )+ΒΏ(0.5 β 4 β3 ) β2ΒΏ 40+ΒΏ30+ΒΏ50+ΒΏ12ΒΏ132ππ2
2 (1β1 )+4 (3 β1 )=14 ππ2
(5 β10 )+(5 β8 )+ (5 β6 )+2 (0.5 β6Γ8 )ΒΏ168ππ2
6 (6 β6)=216ππ2
(12 β5 )+(12β 4 )+ (12 β3 )+2 (0.5 β3Γ4 )ΒΏ156ππ2
2 (2 β8 )+2 (11 β8 )+2 (2 β11 )=252ππ2
(7 β13 )+(7 β12 )+(7 β5 )+2 (0.5 β5Γ12 )ΒΏ270ππ2
Square-Based PyramidsLetβs have a look at the square based pyramid.
πππ
πππ
This should be easy to calculate the surface area with too!
Example
4ππ7ππ
4ππ7ππ
Surface Area:
42+ΒΏ(4 β7 β 12 )β 4ΒΏ16+56ΒΏ72ππ2
Square-Based Pyramids
40ππ2 45π2 161ππ2
56ππ2 105ππ2 1035ππ2
Letβs calculate the surface area of a cylinder with its radius and length.Example
ππ
ΒΏ2πΒΏ10π
We know the cylinder is made of two and, if flattened a
.
circlesrectangl
e
2π10π
πΆ=2π π4ππ
Cylinders
2π10π
πΆ=2π π4ππ
S.A =
ΒΏ8π+40πΒΏ 48ππ2
Note: Formulae for surface area will not be provided on the test as calculations are simply sums of areas of polygons and circles. Some formulae for polygons and circles will be provided.
Cylinders
48πππ2 152πππ2 84 ππ2
3.5ππ2 480πππ2 16π ππ2
Answers