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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 2018 HSC 30a

A cylindrical oil tank has a height of 7 metres and a capacity of 1.5 megalitres.
 

What is the diameter of the oil tank? Give your answer in metres, correct to two decimal places.  (3 marks)

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`16.50\ text{m}`

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`text{Converting megalitres to m³  (using 1 m³ = 1000 L):}`

♦ Mean mark 48%.

`1.5\ text(ML)` `= (1.5 xx 10^6)/(10^3)`
  `= 1.5 xx 10^3\ text(m)^3`
  `= 1500\ text(m)^3`

 

`V` `= pir^2h`
`1500` `= pi xx r^2 xx 7`
`r^2` `= 1500/(pi xx 7)`
`sqrt(r^2)` `= sqrt(68.21)`
  `= 8.26\ text{m}`

 

`text{Diameter}` `=2r`  
  `=2xx8.26 \ text{m}`  
  `=16.52\ text{m}`  

 

Measurement, STD2 M1 2018 HSC 30a

A cylindrical water tank has a radius of 9 metres and a capacity of 1.26 megalitres.
 

What is the height of the water tank? Give your answer in metres, correct to two decimal places.  (3 marks)

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`4.95\ text{m}`

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`text{Converting megalitres to m³  (using 1 m³ = 1000 L):}`

♦ Mean mark 48%.

`1.26\ text(ML)` `= (1.26 xx 10^6)/(10^3)`
  `= 1.26 xx 10^3\ text(m)^3`
  `= 1260\ text(m)^3`

 

`V` `= pir^2h`
`1260` `= pi xx 9^2 xx h`
`h` `= 1260/(pi xx 9^2)`
  `= 4.951…`
  `= 4.95\ text{m  (2 d.p.)}`

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) 

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`581\ text(L)`

Show Worked Solution

`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)}`