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Algebra, NAP-C4-CA32 SA

The surface area of a brick is given by the rule:

total surface area = 2 × [(width × height) + (width × length) + (height × length)]

The brick shown has a total surface area of 982 square centimetres.
 

 

What is the width of the brick?

   centimetres
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`10.5\ text(cm)`

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`text(Let)\ \ w = text(width of the brick)`

`text(Surface Area)` `= 2 xx [8w + 22w + (8 xx 22)]`
`982` `= 2(30w + 176)`
  `= 60w + 352`
`60w` `= 630`
`:. w` `= 10.5\ text(cm)`

Algebra, NAP-D4-CA07

The surface area `(S)` of the prism below can be calculated by multiplying the perimeter of its face `(p)` by its height `(h)`, and adding twice the area of its face `(F)`.
 


 

Which one of these formulas could be used for this calculation?

 
 `S = 2 p h F`
 
 `S = p h + F`
 
 `S = p h + 2F`
 
 `S = 2 ph + 2F`
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`S = p h + 2F`

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`S = p h + 2F`

Measurement, NAP-C4-NC32 SA

The total surface area of a cube is 150 cm².
 

 How long is an edge of the cube?

  cm
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`text(5 cm)`

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`text(Surface area of 1 face of the cube)`

`=150/6`

`=25\ text(cm²)`

 

`text(Let)\ \ x=\ text(length of 1 side)`

`x^2` `=25`
`:.\ x` `=5\ text(cm)`

Measurement, NAP-F4-CA21

A cube has a side length of 6 cm.

Two smaller cubes of side length 3 cm are attached to the larger cube as shown in the diagram below.
  

What is the surface area of the new object?

`216\ text(cm²)` `243\ text(cm²)` `270\ text(cm²)` `288\ text(cm²)`
 
 
 
 
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`270\ text(cm²)`

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`text(One strategy:)`

`text{Calculate the surface area (S.A.) of the 2 objects joined}`

`text(separately and deduct the area where they join.)`
 

`text{S.A. (large cube)} = 6 xx 6xx 6 = 216\ text(cm²)`

`text{S.A. (2 smaller cubes joined together)}`

`=2 xx (3 xx 3) + 4 xx (6 xx 3)`

`=90\ text(cm²)`

`text{S.A. to be deducted (where cubes are attached)}`

`= 2 xx (6 xx 3)`

`= 36\ text(cm²)`

 

`:.\ text{S.A. (new object)}` `= 216 + 90 – 36`
  `=270\ text(cm²)`

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`

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`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`

Measurement, NAP-I4-CA27 SA

A glass aviary is made up of four triangles and a square, as shown in the diagram below.

 naplan-2016-27
Harry is hired to clean the interior sides of the aviary, not including the floor.

What is the area that Harry will need to clean?

   m²
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`402\ text(m²)`

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`text(Area to clean)`

`= 4 xx 1/2 bh`

`= 4 xx 1/2 xx 15 xx 13.4`

`= 402\ text(m²)`