smc-798-60-Water Catchment

v1 Measurement, STD2 M1 2014 HSC 27c

A swimming pool is in the shape of a rectangle with a semicircle at each end, as shown.

The pool is 7000 mm long, 4000 mm wide, and has a depth of 2100 mm.

How much water is needed to fill the pool, to the nearest litre? (4 marks)

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`51 \ 589 \ text(L)`

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`V = Ah`

♦ Mean mark 41%
STRATEGY: Adjusting measurements to metres makes the final conversion to litres simple.

`text(Finding Area of base)`

`text(Semi-circles have radius 2000 mm) = 2 \ text(m)`

`:.\ text(Area of 2 semicircles)`

`=2 xx 1/2 xx pi r^2`

`= pi xx 2^2`

`= 12.56 \ text(m)^2`

`text(Area of rectangle)`

`= l xx b`

`= (7-2 xx 2) xx 4`

`= 12\ text(m)^2`

`:.\ text(Volume)`	`= Ah`
	`= (12.56… + 12) xx 2.1`
	`= 51.589…\ text(m)^3`
	`= 51 \ 589 \ text(L)\ \ text{(using 1m³} = 1000\ text{L)}`

v1 Measurement, STD2 M1 2010 HSC 17 MC

During a heavy storm, 2.4 hectares of farmland received rainfall to a depth of 12 cm.

How many kilolitres of rainwater fell on the farmland? (1 hectare = 10 000 m²)

2.88 kL
2880 kL
288 000 kL
2 880 000 kL

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`B`

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♦♦ Mean mark 36%
NOTE: The unit conversion 1 m³ = 1000 L is contained in the Formulae and Data sheet given out in the exam.

`text(Area of farmland)`	`=2.4xx10\ 000`
	`=24\ 000\ text(m²)`
`text(Volume)`	`=Ah`
	`=24\ 000xx0.12`
	`=2880\ text(m³)`

`text{1 m³}`	`=1000\ text(L)=1\ text(kL)`
`:.\ text(Volume)`	`=2880\ text(kL)`

`=>B`

v1 Measurement, STD2 M1 SM-Bank 26 MC

A rectangular swimming pool measures 15 m by 8 m and has an average depth of 1.8 m. The pool is being filled at a rate of 250 litres per minute.

What is the volume of water needed to fill the pool completely?

(1 m³ = 1000 L)

216 L
2 160 L
21 600 L
216 000 L

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`=>\ text(D)`

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`text(Volume of pool in m³:)`

`text(Vol)`	`= l xx w xx h`
	`= 15 xx 8 xx 1.8`
	`= 216 \ text(m³)`
	`= 216 xx 1000 \ text(L)`
	`= 216\ 000 \ text(L)`

`=>\ text(D)`

v1 Measurement, STD2 M1 2016 HSC 30a

The area of a school roof is 45 m². All rain that falls on the roof flows into a storage tank.

How many litres of water are collected in the tank when 25 mm of rain falls? (2 marks)

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`1125\ \text{L}`

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`text{Volume}`	`= A × h`
	`= 45 × (25 ÷ 1000)`
	`= 1.125\ \text{m}^3`
	`= 1125\ \text{L}`

Measurement, STD2 M1 2022 HSC 28

A dam is in the shape of a triangular prism which is 50 m long, as shown.

Both ends of the dam, `A B C` and `D E F`, are isosceles triangles with equal sides of length 25 metres. The included angles `B A C` and `E D F` are each `150^@`.

Calculate the number of litres of water the dam will hold when full. (4 marks)

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`7\ 812\ 500\ text{L}`

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`V=Ah`

`text{Use sine rule to find}\ A:`

`A`	`=1/2 ab\ sinC`
	`=1/2 xx 25 xx 25 xx sin150^@`
	`=156.25\ text{m}^2`

`:.V`	`=156.25 xx 50`
	`=7812.5\ text{m}^3`

`text{S}text{ince 1 m³ = 1000 litres:}`

`text{Dam capacity}`	`=7812.5 xx 1000`
	`=7\ 812\ 500\ text{L}`

♦♦ Mean mark 33%.

Measurement, STD2 M1 SM-Bank 26 MC

During a flood, 12.5 hectares of land was covered by water to a depth of 30 cm.

How many kilolitres of water covered the land?

(1 hectare = 10 000 m² and 1 m³ = 1000 L)

3.75 kL
37.5 kL
37 500 kL
37 500 000 kL

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`=>\ text(C)`

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`text(Volume of water in m³:)`

`text(Vol)`	`= Ah`
	`= 12.5 xx 10\ 000 xx 30\ text(cm)`
	`= 12.5 xx 10\ 000 xx 0.3`
	`= 37\ 500 \ text(m³)`
	`= 37\ 500\ text(kL)`

`=>\ text(C)`

Measurement, STD2 M1 2016 HSC 30a

The area of a roof is 30 m². Any rain that falls on the roof flows directly onto a garden.

Calculate how many litres of water flow onto the garden when 20 mm of rain falls on the roof. (2 marks)

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`600\ text(L)`

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♦♦ Mean Mark 27%.
STRATEGY: Converting 20 mm into metres as a 1st step is an efficient approach here.

`text(Volume)`	`= Ah`
	`= 30 xx 20/1000`
	`= 0.6\ text(m³)`
	`= 600\ text(L)`

Measurement, STD2 M1 2014 HSC 27c

The base of a water tank is in the shape of a rectangle with a semicircle at each end, as shown.

The tank is 1400 mm long, 560 mm wide, and has a height of 810 mm.

What is the capacity of the tank, to the nearest litre? (4 marks)

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

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`581\ text(L)`

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`V = Ah`

♦ Mean mark 41%
STRATEGY: Adjusting measurements to metres makes the final conversion to litres simple.

`text(Finding Area of base)`

`text(Semi-circles have radius 280 mm) = 0.28\ text(m)`

`:.\ text(Area of 2 semicircles)`

`=2 xx 1/2 xx pi r^2`

`= pi xx (0.28)^2`

`= 0.2463…\ text(m)^2`

`text(Area of rectangle)`

`= l xx b`

`= (1.4-2 xx 0.28) xx 0.56`

`= 0.4704\ text(m)^2`

`:.\ text(Volume)`	`= Ah`
	`= (0.2463… + 0.4704) xx 0.810`
	`= 0.580527…\ text(m)^3`
	`= 580.527…\ text(L)\ \ text{(using 1m³} = 1000\ text{L)}`
	`= 581\ text(L)\ text{(nearest L)}`

Measurement, STD2 M1 2010 HSC 17 MC

During a flood 1.5 hectares of land was covered by water to a depth of 17 cm.

How many kilolitres of water covered the land? (1 hectare = 10 000 m²)

2.55 kL
2550 kL
255 000 kL
2 550 000 kL

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`B`

Show Worked Solution

♦♦ Mean mark 34%
NOTE: The unit conversion 1 m³ = 1000 L is contained in the Formulae and Data sheet given out in the exam.

`text(Area covered)`	`=1.5xx10\ 000`
	`=15\ 000\ text(m²)`
`text(Volume)`	`=Ah`
	`=15\ 000xx0.17`
	`=2550\ text(m³)`

`text{1 m³}`	`=1000\ text(L)=1\ text(kL)`
`:.\ text(Volume)`	`=2550\ text(kL)`

`=>B`