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Measurement, STD1 M5 2019 HSC 20

The plan of the lower level of a small house is shown.


 

  1. How many windows are shown on the plan?  (1 mark)

  2. What is the actual perimeter, in metres, of the shaded part of the kitchen floor?  (2 marks)

Show Answers Only
  1. `text(6 windows)`
  2. `6.5\ text(metres)`
Show Worked Solution

a.   `text(6 windows)`

 

b.    `text(Plan Perimeter)` `= 2 xx 3\ text(units) + 2 xx 3.5\ text(units)`
    `= 13\ text(units)`

 

`:.\ text(Actual perimeter)` `= 13 xx 0.5`
  `= 6.5\ text(metres)`

Measurement, STD2 M7 2015 HSC 29c

The image shows a rectangular farm shed with a flat roof.
 

Measurement, 2UG 2015 HSC 29c

 
The real width of the shed indicated by the dotted line was measured using an online ruler tool, and found to be approximately 12 metres.

  1. By measurement and calculation, show that the area of the roof of the shed is approximately 216 m².  (2 marks)

  2. All the rain that falls onto this roof is diverted into a cylindrical water tank which has a diameter of 3.6 m. During a storm, 5 mm of rain falls onto the roof.

     

    Calculate the increase in the depth of water in the tank due to the rain that falls onto the roof during the storm.  (3 marks)

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  1. `text(See Worked Solutions.)`
  2. `10.6\ text{cm  (to 1 d.p.)}`
Show Worked Solution

i.    `text(By measurement,)`

♦ Mean mark 35%.

`text(Roof length = 1.5 times the roof width)`

`text{Width = 12 m  (given)}`

`text(Length)` `= 1.5 xx 12`
  `= 18\ text(m)`

 

`:.\ text(Area of roof)` `= 12 xx 18`
  `= 216\ text(m²)\ \ text(…as required)`

 

ii.  `text(Volume of water)`

♦♦♦ Mean mark 14%.

`= Ah`

`= 216 xx 0.005\ \ \ (5\ text(mm) = 0.005\ text(m))`

`= 1.08\ text(m³)`
 

`text(Volume of cylinder =)\ pir^2h`

`r = 3.6/2 = 1.8\ text(m)`
 

`text(Find)\ h\ text(when)\ V= 1.08\ text(m³),`

`pi xx 1.8^2 xx h` `= 1.08`
 `:. h` `= 1.08/(pi xx 1.8^2)`
  `= 0.1061…\ text(m)`
  `= 10.6\ text{cm  (to 1 d.p.)}`

Measurement, STD2 M7 2011 HSC 24a

Part of the floor plan of a house is shown. The plan is drawn to scale.

2011 24a

  1. What is the width of the stairwell, in millimetres?   (1 mark)

  2. What are the internal dimensions of the bathroom, in millimetres?    (1 mark)

  3. What is the length `AB`, the internal length of the rumpus room, in millimetres?   (1 mark)

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  1. `900\  text(mm)`
  2. `2000\  text(mm) xx 2000\  text(mm)`
  3. `9695\  text(mm)`
Show Worked Solution
i.      `900\  text(mm)`

 

ii.     `2000\  text(mm) xx 2000\  text(mm)`

 

iii.    `text(Length of Rumpus Room) = AB`
 `AB` `= 3600 + 90 + 2000 + 90 + 3915`
  `=9695\ text(mm)`

Measurement, STD2 M7 2010 HSC 23b

The elevation and floor plan of a building are shown.

2010 23b

Calculate the area of the floor of this building in square metres.   (2 marks)

Show Answers Only

`46\ text(m²)`

Show Worked Solution
MARKER’S COMMENT: Less errors were made by students who converted to metres FIRST, before calculating the area.
`text(Floor Area)` `=text(Area)\ 1+text(Area)\ 2`
  `=(8xx5)+(2xx3) \ \ \ \ text{(1 m = 1000 mm)}`
  `=46\ text(m²)`