l.obj: to explore area and volume functional skills project exploring area & volume

L.Obj: to explore area and volume

Functional skills Project

Exploring Area & 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


Height

WidthDepth

Volume of the Cuboid.....

Width x Height x Depth = Volume in m3


3 m

10 m6 m

Volume of the Cuboid.....

3m x 10m x 6m = 180 m3


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


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.


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


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


A SPACE STATION


What Maths will you need in a colony on another planet?


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.


You will need to complete this sheet using the plans of the new station.


The Station Design


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.


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)

l.obj: to explore area and volume functional skills project exploring area & volume

Documents