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Number, NAP-K4-CA31

A grain silo is in the shape of a cylinder.

The silo has a diameter of 10 metres.

Grain is poured into an empty silo at a rate of 4 cubic metres per minute.
 

 
Approximately how long will it take to completely fill the silo?

`1 3/4\ text(hours)` `2 1/2\ text(hours)` `4\ text(hours)` `16\ text(hours)`
 
 
 
 
Show Answers Only

`4\ text(hours)`

Show Worked Solution

`text(Volume of cylinder)`

`= pi xx r^2 xx h`

`= pi xx 5^2 xx 12`

`~~ 942\ text(m³)`
 

`:.\ text(Time to fill silo)`

`~~ 942 ÷ 4`

`~~ 235\ text(mins)`

`~~ 4\ text(hours)`

Filed Under: Perimeter, Area and Volume, Perimeter, Area and Volume, Rates and Ratios, Rates and Ratios Tagged With: Band 10, smc-3177-65-Rates and geometry, smc-3183-60-Volume – Other, smc-669-60-Volume - Other, smc-685-65-Rates and geometry

Measurement, NAP-J4-CA39 SA

A rectangular prism is made by using 6 identical triangular prisms.
 

  
What is the volume of one rectangular prism, in cubic centimetres?

 cubic centimetres
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`37 200 text(cm³)`

Show Worked Solution

`text(Volume of rectangular prism)`

`= 62 xx 50 xx 72`

`= 223\ 200\ text(cm³)`

 

`:.\ text(Volume of 1 triangular prism)`

`= 223\ 200 ÷ 6`

`= 37\ 200\ text(cm³)`

Filed Under: Perimeter, Area and Volume, Perimeter, Area and Volume Tagged With: Band 10, smc-3183-60-Volume – Other, smc-669-60-Volume - Other

Measurement, NAP-D4-NC30 SA

When 1 mm of rain falls on 1 m²  of a pool, 1 litre of water is collected.

A pool of what surface area is needed to collect 6000 litres from a rainfall of 15 mm?

  m²
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`400`

Show Worked Solution

`text(If 15 mm of rain falls on 1 m²)`

`=> 15\ text(litres collected)`

 

`:.\ text(Surface Area of pool needed)`

`= 6000/15`

`= 400\ text(m²)`

Filed Under: Perimeter, Area and Volume, Perimeter, Area and Volume, Rates and Ratios, Rates and Ratios Tagged With: Band 10, smc-3177-65-Rates and geometry, smc-3183-60-Volume – Other, smc-669-60-Volume - Other, smc-685-65-Rates and geometry

Measurement, NAP-G4-NC10

The flask pictured below can hold up to 100 mL of water.
 

 
How much water is in the flask?

`60\ text(mL)` `70\ text(mL)` `80\ text(mL)`  `90\ text(mL)`
 
 
 
 
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`text(80 mL)`

Show Worked Solution

`text(Flask is fully filled until the 60 mL mark.)`

`text(Flask is half filled between 60-100 mL marks.)`

`:.\ text(Volume of water in the flask)`

`=60 + (1/2 xx 40)`

`=80\ text(mL)`

Filed Under: Perimeter, Area and Volume, Perimeter, Area and Volume, Units of Measurement, Units of Measurement Tagged With: Band 7, smc-3182-10-Scale measure, smc-3183-60-Volume – Other, smc-669-60-Volume - Other, smc-671-10-Scale measure

Measurement, NAP-G4-CA22 SA

Tom cut a tennis ball into two halves.
 

The following calculation gives the approximate volume of one half of the ball in cm³.
 

`text(Volume) = 1/2 xx 4/3 pi xx r^3`
 

What volume does the calculation give, to the nearest cm³, where `r` is the radius of the ball?

   cm³
Show Answers Only

 `90\ text(cm³)`

Show Worked Solution
`V` `= 1/2 xx 4/3 pi xx 3.5^3`
  `= 89.79…`
  `= 90\ text(cm³)`

Filed Under: Perimeter, Area and Volume, Perimeter, Area and Volume Tagged With: Band 9, smc-3183-60-Volume – Other, smc-669-60-Volume - Other

Measurement, NAP-H4-CA07

A shoebox is square at each end and twice as long as it is high, as shown in the diagram.
 

 
Which of these is the closest estimate for the number of cubes that would fill the box?

`16` `60` `130` `500`
 
 
 
 
Show Answers Only

`130`

Show Worked Solution

`text(The box front is around 4 cubes wide and 4 cubes high.)`

`text(Estimated cubes that could fit)`

`=h xx h xx (2h)`

`= 4 xx 4 xx (4 + 4)`

`= 16 xx 8`

`= 128`
 

`:. 130\ text(is the closest.)`

Filed Under: Perimeter, Area and Volume, Perimeter, Area and Volume Tagged With: Band 7, smc-3183-60-Volume – Other, smc-669-60-Volume - Other

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