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Measurement, STD1 M1 2019 HSC 25

The diagram shows a sector with an angle of 120° cut from a circle with radius 10 m.

What is the perimeter of the sector? Write your answer correct to 1 decimal place.  (3 marks)

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`40.9\ \ (text(1 d. p.))`

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`text(Arc length)` `= 120/360 xx 2 xx pi xx 10`
  `= 20.94`

 

`:.\ text(Perimeter)` `= 20.94 + 2 xx 10`
  `= 40.94`
  `= 40.9\ \ (text(1 d. p.))`

Measurement, STD2 M1 2018 HSC 22 MC

A shape consisting of a quadrant and a right-angled triangle is shown.
 

 
What is the perimeter of this shape, correct to one decimal place?

  1. 28.6 cm
  2. 36.6 cm
  3. 66.3 cm
  4. 74.3 cm
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`text(B)`

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`text(Using Pythagoras to find radius)\ (r):`

`r` `= sqrt(10^2 – 6^2)`
  `= sqrt64`
  `= 8\ text(cm)`

 

`text(Arc length)` `= 1/4 xx 2 pi r`
  `= 1/4 xx 2 xx pi xx 8`
  `= 12.56…\ text(cm)`

 

`:.\ text(Perimeter)` `= 8 + 6 + 10 + 12.56…`
  `= 36.57…`

`=>\ text(B)`

Measurement, STD2 M1 2012 HSC 27b

The sector shown has a radius of 13 cm and an angle of 230°. 
 

 2012 27b
 

 What is the perimeter of the sector to the nearest centimetre?    (2 marks) 

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`text(78 cm)\ \ \ \  text((nearest cm))`

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♦ Mean mark 39%
MARKER’S COMMENT: The formula of the length of an arc is given in the formula sheet.
`text(Perimeter)` `= 2 xx text(radius) + text(arc length)`
`text(Arc length)` `= theta/360 xx 2 xx pi xx r`
  `= 230/360 xx 2 xx pi xx 13`
  `= 52.1853…`
   
`:.\ text(Perimeter)` `= 2 xx 13 + 52.1853…`
  `= 78.1853…`
  `=text(78 cm)\ \ \ \ text((nearest cm))`