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Measurement, NAP-G4-CA32

The rectangular prism, shown below, is cut in half to form 2 equal cubes.
 

What is the ratio of the surface area of the rectangular prism to one of the cubes?

`3 : 5` `5 : 3` `1 : 2` `2 : 1`
 
 
 
 
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`5 : 3`

Show Worked Solution

`text(S.A. of rectangular prism)`

`= 2 xx (h xx h) + 4 xx (2h xx h)`

`= 2h^2 + 8h^2`

`= 10 h^2`

 

`text(S.A. of cube)`

`= 6 xx (h xx h)`

`= 6h^2`

 

`:.\ text(Ratio of rectangular prism to cube)`

`= 10h^2 : 6h^2`

`= 5 : 3`

Number, NAP-I4-NC32

Mark and Jim have property sizes as shown in the table below:
  

`text(Property Owner)` `text(Property Size)`
`text(Mark)` `text(1 square kilometre)`
`text(Jim)` `text(5000 square metres)`

  
 What is the ratio of the land area of Mark's property to Jim's property.

`2:1` `5:2` `200:1` `250:1` `4000:1`
 
 
 
 
  
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`200:1`

Show Worked Solution
`text(1 km²)` `= 1000\ text(m × 1000 m)`
  `= 1\ 000\ 000\ text(m²)`

 

`text(Ratio)` `= 1\ 000\ 000: 5000`
  `= 1000:5`
  `= 200:1`