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Measurement, NAP-I4-CA17v1

A wheel on a bicycle has a diameter of 530 mm.
 

naplan-2016-17mci

 
The wheel turns 3 times.

Approximately how many metres has the bicycle travelled?

`text(2 m)` `text(5 m)` `text(10 m)` `text(25 m)`
 
 
 
 
Show Answers Only

`5\ text(m)`

Show Worked Solution
`text(Diameter)` `=530\ text(mm)`
  `=0.530\ text(m)`

 
`:.\ text{Distance (3 rotations)}`

`= 3 xx (pi xx d)`

`= 3 xx (pi xx 0.530)`

`= 4.99…\ text(m)`

`=5\ text{m  (nearest m)}` 

Filed Under: Perimeter, Area and Volume Tagged With: Band 8, smc-3153-15-Perimeter (Circular)

Measurement, NAP-F4-CA16v1

A car tyre has a circumference of 120 cm.

Which of these is closest to the radius of the tyre?

`9.5\ text(cm)` `19.1\ text(cm)` `38.0\ text(cm)` `753.6\ text(cm)`
 
 
 
 
Show Answers Only

`19.1\ text(cm)`

Show Worked Solution
`C` `= 2 pi r`
`120` `=2 xx pi xx r`
`r` `=120/(2 pi)`
  `~~19.1\ text(cm)`

Filed Under: Perimeter, Area and Volume Tagged With: Band 8, smc-3153-15-Perimeter (Circular)

Measurement, NAP-A4-CA15v1

Angelique painted a circle with a radius of 5.6 cm.

What is the circumference of the circle to the nearest centimetre?

`text(11 cm)` `text(17 cm)` `text(18 cm)` `text(35 cm)`
 
 
 
 
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`text(35 cm)`

Show Worked Solution
`C` `= 2pir`
  `= 2 xx pi xx 5.6`
  `= 35.185…\ text(cm)`

Filed Under: Perimeter, Area and Volume Tagged With: smc-3153-15-Perimeter (Circular)

Measurement, NAP-K4-CA26 SA

Percy has a large shower head which has a diameter of 25.5 centimetres.

What is the circumference of the shower head in centimetres, to one decimal place?
 


 

    cm
Show Answers Only

`80.1\ text(cm)`

Show Worked Solution
`text(Circumference)` `= pi xx d`
  `= pi xx 25.5`
  `= 80.110`
  `= 80.1\ text(cm)`

Filed Under: Perimeter, Area and Volume, Perimeter, Area and Volume, Perimeter, Area and Volume Tagged With: Band 10, smc-3153-15-Perimeter (Circular), smc-3183-15-Perimeter (Circular), smc-669-15-Perimeter (Circular)

Measurement, NAP-B4-CA25

A yoyo at the end of a string moves through a quarter circle, as shown below.

The string is 70 cm long.
 

 
The curved distance the yoyo has travelled is closest to

`text(80 cm)` `text(90 cm)` `text(100 cm)` `text(110 cm)`
 
 
 
 
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`110`

Show Worked Solution
`text(Distance)` `= 1/4 xx 2pir`
  `= 1/4 xx 2 xx pi xx 70`
  `= 109.95…`
  `~~ 110\ text(cm)`

Filed Under: Perimeter, Area and Volume, Perimeter, Area and Volume, Perimeter, Area and Volume Tagged With: Band 9, smc-3153-15-Perimeter (Circular), smc-3183-15-Perimeter (Circular), smc-669-15-Perimeter (Circular)

Measurement, NAP-E4-CA13

Grant cut two semicircles from a rectangle to create Shape 1.

He then joins the semicircles to each end of an identical rectangle to create Shape 2.

Which of the following statements is true about Shape 1 and Shape 2?

 
They have the same area and the same perimeter.
 
They have different areas and the same perimeter.
 
They have the same area and different perimeters.
 
They have different areas and different perimeters.
Show Answers Only

`text(They have different areas and the same perimeter.)`

Show Worked Solution

`text(The semi-circles in both shapes have the same length)`

`text(but have been turned around in Shape 2.)`

`:.\ text(They have different areas and the same perimeter.)`

Filed Under: Perimeter, Area and Volume, Perimeter, Area and Volume, Perimeter, Area and Volume Tagged With: Band 8, smc-3153-15-Perimeter (Circular), smc-3153-25-Area (Circular), smc-3183-15-Perimeter (Circular), smc-3183-25-Area (Circular), smc-669-15-Perimeter (Circular), smc-669-25-Area (Circular)

Measurement, NAP-D4-CA25

Guerra slings a fire torch in a circle at the end of a 3 metre rope.
 

 
About how far has the fire torch travelled after completing 15 circles?

`text(30 metres)` `text(45 metres)` `text(140 metres)` `text(280 metres)`
 
 
 
 
Show Answers Only

`text(280 metres)`

Show Worked Solution
`C` `= 2 pi r`
  `= 2 xx pi xx 3` 
  `= 18.85…`

 

`:.\ text(Distance travelled in 15 circles)`

`=15 xx 18.85…`

`= 282.74…`

`~~280\ text(metres)`

Filed Under: Perimeter, Area and Volume, Perimeter, Area and Volume, Perimeter, Area and Volume Tagged With: Band 9, smc-3153-15-Perimeter (Circular), smc-3183-15-Perimeter (Circular), smc-669-15-Perimeter (Circular)

Measurement, NAP-H4-CA32 SA

Pedro cuts a sector from a circle so that  `3/8`  of the area of the circle remains.
 


 

If the circle's radius is 5 cm, what is the perimeter of the shape, to the nearest centimetre?

   cm
Show Answers Only

`22\ text(cm)`

Show Worked Solution
`text(Perimeter)` `= 3/8 xx 2 pi r + 2 r`
  `= 3/8 xx 2 pi xx 5 + 10`
  `= 21.78…`
  `= 22\ text{cm  (nearest cm)}`

Filed Under: Perimeter, Area and Volume, Perimeter, Area and Volume, Perimeter, Area and Volume Tagged With: Band 10, smc-3153-15-Perimeter (Circular), smc-3183-15-Perimeter (Circular), smc-669-15-Perimeter (Circular)

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