Square and Cubic Units


This chapter explores square and cubic units. The objectives of this chapter are; to be able to convert between different units of area and volume, and solve area, volume and capacity problems with mixed units. Before attempting this chapter you must have prior knowledge of units of length, area, volume and the standard form.

Square Units

The shape below is a square and has sides of 1 cm. Square and Cubic Units-01 The area for the square is; Square and Cubic Units-02 Suppose we wanted to use mm instead of 1cm. The units have been converted from cm to mm below; Square and Cubic Units-03 The area in mm is now; Square and Cubic Units-04 It is therefore logical to say that 1cm² is equal to 100mm ². Square and Cubic Units-05 With knowledge of the fact explored above you can use the fact to convert areas for example; Square and Cubic Units-06 …and… Square and Cubic Units-07 Let’s look at a different unit. Below is a square with sides of 11km. Square and Cubic Units-08 The area for square is; Square and Cubic Units-09 Suppose we use metres instead of kilometers. Below the square the square units have been converted to metres. Square and Cubic Units-10 The above shows us that; Square and Cubic Units-11 Suppose the above value is so big it is a good idea to use standard form. Square and Cubic Units-12 In this example we can use the conversation to work out that; Square and Cubic Units-13 Here is another example; Square and Cubic Units-14 Above you may have noticed a pattern which we can use as the general when dealing with square units. In general when dealing with square units you need to square the conversation factor too for example; Square and Cubic Units-15 …that means; Square and Cubic Units-16 Here is another example; Square and Cubic Units-17 …that means… Square and Cubic Units-18

Cubic Units

The cube below has edges of 1cm. Square and Cubic Units-19 Suppose we wanted to find the volume. The volume would be; Square and Cubic Units-20 What if we converted the units from cm to mm. The cube units have been changed to mm as shown below; Square and Cubic Units-21 The volume in mm would now be; Square and Cubic Units-22 We can conclude that; Square and Cubic Units-23 Let’s explore an example for the above conclusion. Square and Cubic Units-24 Here is another example; Square and Cubic Units-25

Capacity problem

Here is an example based on what is explored above. An oil tank is in the shape of a cuboid. It measures 5m x 4.7m x 3.3m. How many litres of oil can the tank hold when full? Square and Cubic Units-26 We know that; Square and Cubic Units-27 First we calculate the volume of the tank in m3 so the volume is; Square and Cubic Units-28 Next we convert the units into cm3 Square and Cubic Units-29 Every 1000cm3 makes 1 litre therefore; Square and Cubic Units-30 So the volume is 7.55 x 103 litres we can convert the number into standard from at the moment it is not. When writing standard forms the number at the front needs to be between 1 and 10. So we must divide 77.55 by 10. Square and Cubic Units-31 Since we divided 77.55 by 10 we must increase the power at the end by 1 to compensate. Or simply multiply 103 by 10 since we divided. The result is; Square and Cubic Units-32 ;
//Comments This chapter explores square and cubic units. The objectives of this chapter are; to be able to convert between different units of area and volume, and solve area, volume and capacity problems with mixed units. Before attempting this chapter you must have prior knowledge of units of length, area, volume and the standard form.

Square Units

The shape below is a square and has sides of 1 cm. Square and Cubic Units-01 The area for the square is; Square and Cubic Units-02 Suppose we wanted to use mm instead of 1cm. The units have been converted from cm to mm below; Square and Cubic Units-03 The area in mm is now; Square and Cubic Units-04 It is therefore logical to say that 1cm² is equal to 100mm ². Square and Cubic Units-05 With knowledge of the fact explored above you can use the fact to convert areas for example; Square and Cubic Units-06 …and… Square and Cubic Units-07 Let’s look at a different unit. Below is a square with sides of 11km. Square and Cubic Units-08 The area for square is; Square and Cubic Units-09 Suppose we use metres instead of kilometers. Below the square the square units have been converted to metres. Square and Cubic Units-10 The above shows us that; Square and Cubic Units-11 Suppose the above value is so big it is a good idea to use standard form. Square and Cubic Units-12 In this example we can use the conversation to work out that; Square and Cubic Units-13 Here is another example; Square and Cubic Units-14 Above you may have noticed a pattern which we can use as the general when dealing with square units. In general when dealing with square units you need to square the conversation factor too for example; Square and Cubic Units-15 …that means; Square and Cubic Units-16 Here is another example; Square and Cubic Units-17 …that means… Square and Cubic Units-18

Cubic Units

The cube below has edges of 1cm. Square and Cubic Units-19 Suppose we wanted to find the volume. The volume would be; Square and Cubic Units-20 What if we converted the units from cm to mm. The cube units have been changed to mm as shown below; Square and Cubic Units-21 The volume in mm would now be; Square and Cubic Units-22 We can conclude that; Square and Cubic Units-23 Let’s explore an example for the above conclusion. Square and Cubic Units-24 Here is another example; Square and Cubic Units-25

Capacity problem

Here is an example based on what is explored above. An oil tank is in the shape of a cuboid. It measures 5m x 4.7m x 3.3m. How many litres of oil can the tank hold when full? Square and Cubic Units-26 We know that; Square and Cubic Units-27 First we calculate the volume of the tank in m3 so the volume is; Square and Cubic Units-28 Next we convert the units into cm3 Square and Cubic Units-29 Every 1000cm3 makes 1 litre therefore; Square and Cubic Units-30 So the volume is 7.55 x 103 litres we can convert the number into standard from at the moment it is not. When writing standard forms the number at the front needs to be between 1 and 10. So we must divide 77.55 by 10. Square and Cubic Units-31 Since we divided 77.55 by 10 we must increase the power at the end by 1 to compensate. Or simply multiply 103 by 10 since we divided. The result is; Square and Cubic Units-32 ;
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