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Area, SMB-015

A letterbox, which has been constructed by joining a half cylinder and rectangular prism, needs to be painted on each external surface.
 

Find the surface area of the letterbox, giving your answer correct to the nearest square centimetre.   (3 marks)

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`9061\ text(cm)^2`

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`text{Surface Area (half cylinder)}` `= \frac{1}{2} (2pi r^2 + 2pi rh)`
  `= \frac{1}{2} (2pi xx 17.5^2 + 2pi xx 17.5 xx 40)`
  `= 3161.227…\ text{cm}^2`

 

`text{Area (rest)}` `= (35 xx 40)+2(35 xx 30) + 2(40 xx 30)`  
  `=1400+2(1050)+2(1200)`  
  `=5900\ text{cm}^2`  

 
`text{SA (total)}\ = 3161 + 5900 = 9061\ text{cm}^2`

Area, SMB-014

Calculate the surface area of the half-cylinder below (including the base), giving your answer correct to two decimal places.   (3 marks)
 

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`848.29\ text(m)^2`

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`text(Surface Area)` `= \frac{1}{2} (2pi r^2 + 2pi rh) + (7 xx 45)`
  `= \frac{1}{2} (2pi xx 3.5^2 + 2pi xx 3.5 xx 45) + 315`
  `= 848.285…`
  `= 848.29\ \text{m}^2\ \ text{(2 d.p.)}`

Area, SMB-013

Calculate the surface area of the cylinder below, giving your answer correct to two decimal places.   (2 marks)
 

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`58.31\ text(m)^2`

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`text(Surface Area)` `= 2pi r^2 + 2pi rh`
  `= 2pi (1.6)^2 + 2 pi xx 1.6 xx 4.2`
  `= 58.307…`
  `= 58.31\ \text{m}^2\ \ text{(2 d.p.)}`

Measurement, STD2 M1 2012 HSC 25 MC

The solid shown is made of a cylinder with a hemisphere (half a sphere) on top.
 

What is the total surface area of the solid, to the nearest square centimetre?

  1. 628 cm²
  2. 679 cm²
  3. 729 cm²
  4. 829 cm²
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`B`

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`text(Total surface area)`

`= pir^2 + 2pirh + 1/2 xx 4pir^2`

`= pi xx 4^2 + 2pi xx 4 xx 21 + 1/2 xx 4pi xx 4^2`

`= 678.58…\ text(cm²)`

`=> B`

Measurement, STD2 M1 2018 HSC 27c

A shade shelter is to be constructed in the shape of half a cylinder with open ends. The diameter is 3.8 m and the length is 10 m.
 

 
The curved roof is to be made of plastic sheeting.

What area of plastic sheeting is required, to the nearest m²?  (2 marks)

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`60\ text(m²  (nearest m²))`

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`text(Flatten out the half cylinder,)`

`text(Width)` `= 1/2 xx text(circumference)`
  `= 1/2 xx pi xx 3.8`
  `= 5.969…`

 

`:.\ text(Sheeting required)` `= 10 xx 5.969…`
  `= 59.69…`
  `= 60\ text(m²  (nearest m²))`

Measurement, STD2 M1 2014 HSC 25 MC

A grain silo is made up of a cylinder with a hemisphere (half a sphere) on top. The outside of the silo is to be painted.
  

 What is the area to be painted?

  1. `8143\ text(m²)`
  2. `11\ 762\ text(m²)`
  3. `12\ 667\ text(m²)`
  4. `23\ 524\ text(m²)`
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`A`

Show Worked Solution

`text(Total Area) = text(Area of cylinder) + text(½ sphere)`

♦ Mean mark 40%
`text(Area of cylinder)` `= 2 pi rh`
  `= 2pi xx 24 xx 30`
  `= 4523.9`
`text(Area of ½ sphere)` `= 1/2 xx 4 pi r^2`
  `= 1/2 xx 4 pi xx 24^2`
  `= 3619.1`
`:.\ text(Total area)` `= 4523.9 + 3619.1`
  `= 8143\ text(m²)`

`=>  A`