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
15𝑐𝑚249𝑐𝑚28𝑐𝑚2
108𝑐𝑚291𝑐𝑚2
70𝑐𝑚2
26𝑐𝑚2
135𝑐𝑚2204 𝑐𝑚2
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
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
= = =
Surface Area – 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 ∙4 )+¿(10 ∙3 )+¿(10 ∙5 )+¿(0.5 ∙ 4 ∙3 ) ∙2
= 30+¿50+¿12=
Answers
14𝑐𝑚2
168𝑐𝑚2 216𝑐𝑚2
156𝑐𝑚2252𝑐𝑚2 270𝑐𝑚2
Square-Based PyramidsLet’s have a look at the square based pyramid.
𝑎𝑎𝑠
𝑎𝑎𝑠
This should be easy to calculate the surface area with too!
Square-Based PyramidsExample
4𝑐𝑚
7𝑐𝑚4𝑐𝑚
7𝑐𝑚
Surface area =
42+¿(4 ∙7 ∙ 12 )∙ 4¿16+56¿72𝑐𝑚2
CylindersLet’s calculate the surface area of a cylinder with its radius and length.Example
𝑟𝑙
¿2𝑚¿10𝑚
We know the cylinder is made of two and, if flattened a
.
circlesrectangl
e
2𝑚10𝑚
𝐶=2𝜋 𝑟4𝜋𝑚
Cylinders
2𝑚10𝑚
𝐶=2𝜋 𝑟4𝜋𝑚
S.A =
¿8𝜋+40𝜋¿ 48𝜋𝑚2
On your test you won’t receive any formulae for surface area as the calculations are somewhat obvious but you are welcome to remember some if you need to!
Answers
40𝑐𝑚2 45𝑚2 161𝑚𝑚2
56𝑐𝑚2 105𝑘𝑚2 1035𝑘𝑚2
Answers
48𝜋𝑐𝑚2 152𝜋𝑐𝑚2 84 𝜋𝑚2
3.5𝜋𝑚2 480𝜋𝑚𝑚2 16𝜋𝑘𝑚2