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{m (1 d. p.)}`

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

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

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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`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.

`theta/360`	`= 5700/(2pi xx 6400)`
`theta`	`= (5700 xx 360)/(2pi xx 6400)~~ 51^(circ)`

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

`=>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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`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…`

`=> 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 (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(Perimeter)= 2 xx 13 + 52.1853…= 78.1853…=text{78 cm (nearest cm)}`