smc-6483-40-Perimeter (Circular Measure)

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`

The coordinates of city A are (39°N, 75°W). City B lies on the same longitude and is 5700 km south of city A.

What is the latitude of city B, given the earth's radius is 6400 km?

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`text(D)`

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`text(Circumference) = 2 xx pi xx 6400`

♦ Mean mark 45%.
COMMENT: If the earth’s radius is stated, this past question is arguably within the scope of the new syllabus.

`:. text(City)\ B\ text(is 12° South.)`

`=>\ text(D)`

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?

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`text(B)`

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

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

`=>\ text(B)`

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

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

--- 4 WORK AREA LINES (style=lined) ---

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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))`