SmarterEd

Aussie Maths & Science Teachers: Save your time with SmarterEd

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
Show Answers Only

`165\ text(cm³)`

Show Worked Solution

`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-D4-CA11

Two bricks can be joined to make three different rectangular prisms. Two of them are shown here.
 

 
What would be the measurements of the third prism?

 
 `text(18 cm by 16 cm by 7 cm)`
 
 `text(36 cm by 8 cm by 7 cm)`
 
 `text(32 cm by 18 cm by 7 cm)`
 
 `text(36 cm by 14 cm by 8 cm)`
Show Answers Only

`text(36 cm by 8 cm by 7 cm)`

Show Worked Solution

`text(36 cm by 8 cm by 7 cm)`

Measurement, NAP-E4-CA32 SA

Two views of a trapezoidal prism are shown below.

Each square on this grid has an area of one square centimetre.

The vertical edges of the prism are 4 centimetres.

What is the volume of the prism in cubic centimetres?

   cubic centimetres
Show Answers Only

`72\ text(cm³)`

Show Worked Solution

`text(The area of the base)`

`= 12\ text(squares) + 9\ text(triangles)\ (1 xx 1) + 1\ text(triangle)\ (1 xx 3)`

`= 12 + (9 xx 1/2) + 1 1/2`

`= 18\ text(cm²)`

 

`:.\ text(Volume)` `=18 xx 4`
  `=72\ 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
Show Answers Only

`24\ text(cm)`

Show Worked Solution
`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)`

Measurement, NAP-E4-NC31 SA

Guy uses a rectangular prism pictured below as a basic building block.
 

 

 
He stacks the blocks and makes a solid cube.

What is the smallest possible number of blocks needed to make a cube?
Show Answers Only

`144`

Show Worked Solution

`text(The smallest cube will have the)`

`text(smallest base:)`

 

`text(Base will have 12 blocks.)`

`text(Cube will have 12 stacked levels.)`

 

`:.\ text(Blocks needed for the smallest cube)`

`= 12 xx 12`

`= 144`

Measurement, NAP-F4-CA31 SA

Barry pours two identical cubes of cement as foundation for a large sculpture, as shown in the diagram below.
 

 
If 432 cubic metres are required to form the foundation, what is the height of the foundation, as shown on the diagram?

   metres
Show Answers Only

`12\ text(metres)`

Show Worked Solution

`text(Let dimensions of one cube) = x xx x xx x`

`2x^3` `= 432`
`x^3` `= 216`
`x` `= 6\ text(m)`

 

`:. h` `= 2x`
  `= 12\ text(metres)`

Measurement, NAP-F4-NC29

A wheelchair ramp is pictured below.
 

 
The ramp is in the shape of a triangular prism?

What is the volume of the ramp?

`7.2\ text(m³)` `3.6\ text(m³)` `0.72\ text(m³)` `0.36\ text(m³)`
 
 
 
 
Show Answers Only

`3.6\ text(m³)`

Show Worked Solution
`text(Volume)` `= (1/2 xx 6 xx 0.6) xx 2`
  `= 1.8 xx 2`
  `= 3.6\ text(m³)`

 

Measurement, NAP-H4-NC29 SA

A rectangular trough in a paddock provides water for horses.

Its measurements can be seen below:
  

 
 

One cubic metre holds 1000 litres of water.

How many litres of water will fill the trough?

   litres
Show Answers Only

`text(3000 litres)`

Show Worked Solution
`text(Volume)` `= 8 xx 0.5 xx 0.75`
  `= 4 xx 0.75`
  `= 3\ text(m²)`
  `= 3000\ text(litres)`

Measurement, NAP-H4-CA25 SA

A large sculpture is made in the shape of a cube.

The total length of all of its edges is 60 metres.

What is the volume of the cube?

   m³
Show Answers Only

`125\ text(m³)`

Show Worked Solution

`text(A cube has 12 edges.)`

`:.\ text(Length of 1 edge) = 60/12 = 5\ text(m)`

 

`:.\ text(Volume of cube)` `= 5 xx 5 xx 5`
  `= 125\ text(m³)`

Measurement, NAP-I4-CA30 SA

A box in the shape of a triangular prism is used to store smaller triangular prism pieces as shown below.

 naplan-2016-30i

Each smaller triangular prism is 40 cm³  in size.
 

 naplan-2016-30ii

What is the maximum number of smaller triangular prisms that can fit inside the box?
Show Answers Only

`text(17 pieces)`

Show Worked Solution

`text(Volume of 1 piece)\ = 1/2 xx 6 xx 7.9 xx text(Width)`

`text(Width)` `= 40/(1/2 xx 6 xx 7.9)`
  `= 1.688\ text(cm)`

 

 `:.\ text(Maximum number of pieces that fit)`

`= 30/1.688`

`= 17.77`

`= 17\ \ text{(round down)}`