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L.Obj: to explore area and volume
Functional skills Project
Exploring Area & Volume
L.Obj: to explore area and volume
How wide the shape isHow high the shape isHow deep the shape is
This is a cuboid, it has three “Dimensions” or lengths.
They are...
Height
WidthDepth
L.Obj: to explore area and volume
Height
WidthDepth
Volume of the Cuboid.....
Width x Height x Depth = Volume in m3
L.Obj: to explore area and volume
3 m
10 m6 m
Volume of the Cuboid.....
3m x 10m x 6m = 180 m3
L.Obj: to explore area and volume
We will not need to work out how big the Area of the base is in this task, because we only need the Area that
is exposed to the rays of the Sun.
For the Surface Area we find out how big the area of the surface is
(just like it says on the tin!)
Height
WidthDepth
L.Obj: to explore area and volume
Top
Front
Back
RightLeft
In this task we will not need to know the area of the bottom because it is on the surface of the planet and not exposed to the harmful rays of the sun.
Calculate the area (Width x Height) of each of the 5 faces of the cuboid and then add them together.
L.Obj: to explore area and volume
3 m
10 m6 m
Surface Area (remember no bottom)
Top - 10m x 6m = 60 m2 Left - 3m x 6m = 18m2 Right - 3m x 6m = 18 m2 Front - 10m x 3m = 30 m2 Back - 10m x 3m = 30 m2 Total = 156 m2
L.Obj: to explore area and volume
4 m
8 m3 m
Volume of the Shape
Volume = 4 m x 8 m x 3 m = 96 m3
Surface Area (remember no bottom)
Top - 8m x 3m = 24 m2 Left - 3m x 4m = 12 m2 Right - 3m x 4m = 12 m2 Front - 8m x 4m = 32 m2 Back - 8m x 4m = 32 m2 Total = 112 m2
YOUR TURN
L.Obj: to explore area and volume
L.Obj: to explore area and volume
A SPACE STATION
L.Obj: to explore area and volume
What Maths will you need in a colony on another planet?
L.Obj: to explore area and volume
You will be given the design of a new space station.
It is made up of cuboids, and contains everything that will be needed for the 40 hardy volunteers to live on and thrive on a new planet, Veget.
Your task is to calculate the surface area of the separate domes that will shield the colonists from radiation, the volume of air contained within the whole complex because the outside atmosphere is not breathable and the area of floor space contained inside the habitat shells where the first real Vegetarians will live.
L.Obj: to explore area and volume
You will need to complete this sheet using the plans of the new station.
L.Obj: to explore area and volume
The Station Design
L.Obj: to explore area and volume
Task 2.
The design team are not happy with their Station.
Space U.K. Has agreed to fund additional radiation protective shielding up to a maximum of 3000 m2 for you to increase the size of the colony.
You can change all of the container sizes, with the exception that you may only increase the Heights Widths and Lengths.
You need to get as many colonists living in the colony as possible.
L.Obj: to explore area and volume
Task 3.
Using your design and the original plan, provide the financiers of S.U.K. with details of how you have changed the living habitat.
Compare the original design with your “improved” design by using percentages, fractions and decimals (answering the questions on task sheet 3 will help you to sell your design to the people with the money)