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Measurement, NAP-K4-CA30 SA

Hugo makes a rectangular prism by folding the net below.
 

 

What is the volume of Hugo's rectangular prism?

     cm³
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`165\ text(cm³)`

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`text(Strategy 1)`

`text(By inspection, possible dimensions are:)`

`3 xx 11, 5 xx 11 and 3 xx 5`

`:.\ text(Volume)` `= 3 xx 11 xx 5`
  `= 165\ text(cm³)`

 
`text{Strategy 2 (Algebra)}`

`text(Dimensions of 3 rectangles are:)`

`x xx y = 33\ …\ (1) => y = 33/x …\ (1 prime)`

`x xx h = 55\ …\ (2) => h = 55/x …\ (2 prime)`

`y xx h = 15\ …\ (3)`

 
`text(Substitute)\ (1 prime) and (2 prime)\ text(into)\ (3)`

`33/x xx 55/x` `= 15`
`x^2` `= (33 xx 55)/15`
  `= 121`
`x` `= 11`

 
`=> y = 3, quad h = 5`
  

`:.\ text(Volume)` `= 3 xx 11 xx 5`
  `= 165\ text(cm³)`

Measurement, NAP-E4-CA31 SA

A net of a cube is pictured below.

The cube has a volume of 512 cubic centimetres.

What is the height of the net in centimetres? 

   centimetres
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`24\ text(cm)`

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`text(Let)\ \ s` `=\ text(length of 1 side of the cube)`
`s^3` `= 512`
`:. s` `= 8\ text(cm)`

 

`:.\ text(Height of net)` `= 3 xx 8`
  `= 24\ text(cm)`