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Surface Area
Slideshow 49, Mathematics
Mr Richard Sasaki
Room 307
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Objectivesβ’ Review how to find the area of
various polygons
β’ 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
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Answers
15ππ249ππ28ππ2
108ππ291ππ2
70ππ2
26ππ2
135ππ2204 ππ2
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Surface Area
What 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.
5 cm
2 cm
3 cm 5
cm
2 cm
3 cm
2 cm
3 cm
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Surface Area - Cuboid
5 cm
2 cm
3 cm 5
cm
2 cm
3 cm
2 cm
3 cm
All we do is add the total area of each face.
10 cm2
15 cm2
10 cm2
6 cm2 6 cm215 cm2
We just simply add the numbers together.10 + 15 + 10 + 15 + 6 + 6
= = =
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Surface Area β Triangular Prism
Visualising a net is always good!
4 cm
10 cm
5 cm
3 cm
10 cm
4 cm3 cm5 cm3 cm
4 cm
Surface Area: (10 β4 )+ΒΏ(10 β3 )+ΒΏ(10 β5 )+ΒΏ(0.5 β 4 β3 ) β2
= 30+ΒΏ50+ΒΏ12=
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Answers
14ππ2
168ππ2 216ππ2
156ππ2252ππ2 270ππ2
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Square-Based PyramidsLetβs have a look at the square based pyramid.
πππ
πππ
This should be easy to calculate the surface area with too!
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Square-Based PyramidsExample
4ππ
7ππ4ππ
7ππ
Surface area =
42+ΒΏ(4 β7 β 12 )β 4ΒΏ16+56ΒΏ72ππ2
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CylindersLetβs 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
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Cylinders
2π10π
πΆ=2π π4ππ
S.A =
ΒΏ8π+40πΒΏ 48ππ2
On your test you wonβt receive any formulae for surface area as the calculations are somewhat obvious but you are welcome to remember some if you need to!
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Answers
40ππ2 45π2 161ππ2
56ππ2 105ππ2 1035ππ2
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Answers
48πππ2 152πππ2 84 ππ2
3.5ππ2 480πππ2 16πππ2