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Unit Conversion, SM-Bank 023

  1. By considering the dimensions of a square with an area of 1 square kilometre, complete the unit conversion equation below:

1 km² = ________ m  ×  ________ m = ______________ km²   (1 mark)

  1. The Barangaroo precinct in Sydney has a total floor space of 681 000 square metres.
  2. Find the area of this floor space in square kilometres.  (1 mark)
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a.    \(1\ \text{km}^{2} = 1000\ \text{m}\ \times\ 1000\ \text{m}\ = 1\ 000\ 000\ \text{km}^{2} \)

b.    \(0.681\ \text{km}^{2}\)

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a.    \(1\ \text{km}^{2} = 1000\ \text{m}\ \times\ 1000\ \text{m}\ = 1\ 000\ 000\ \text{km}^{2} \)
 

b.    \(\text{Area}\) \(= \dfrac{681\ 000}{1\ 000\ 000}\)  
  \(=0.681\ \text{km}^{2}\)  

Unit Conversion, SM-Bank 022

  1. By considering the dimensions of a square with an area of 1 square kilometre, complete the unit conversion equation below:

1 km² = _______ m  ×  _______ m = ____________ km²   (1 mark)

  1. A rural property is in the shape of a rectangle with sides of length 1.20 kilometres and 2.36 kilometres.
  2. Find the area of the property in square kilometres and using the conversion equation, express the area in square metres.  (2 marks)
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a.    \(1\ \text{km}^{2} = 1000\ \text{m}\ \times\ 1000\ \text{m}\ = 1\ 000\ 000\ \text{km}^{2} \)

b.    \(2\ 832\ 000\ \text{m}^{2}\)

Show Worked Solution

a.    \(1\ \text{km}^{2} = 1000\ \text{m}\ \times\ 1000\ \text{m}\ = 1\ 000\ 000\ \text{km}^{2} \)
 

b.    \(\text{Area}\) \(= 1.20 \times 2.36\)  
  \(=2.832\ \text{km}^{2}\)  
  \(=2.832 \times 1\ 000\ 000\  \text{m}^{2}\)  
  \(=2\ 832\ 000\ \text{m}^{2}\)  

Unit Conversion, SM-Bank 010

A circle is drawn from a city centre with a radius of 800 metres.

Using the conversion ratio, 1 km² = 1 000 000 m², determine the area of the circle in square kilometres, to two decimal places.  (2 marks)

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\( 2.01 \text{km}^{2}\)

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\(\text{Area}\) \(= \pi \times 800^{2}\ \text{m}^{2} \)  
  \(= 2\ 010\ 619\ \text{m}^{2}\)  
  \(= \dfrac{2\ 010\ 619}{1\ 000\ 000} \)  
  \(=2.01\ \text{km}^{2} \)  

Unit Conversion, SM-Bank 009

A Queensland outback pastoralist owns a property with an area of 500 square kilometres.

Using the conversion ratio, 1 km² = 1 000 000 m², determine the exact area of the property in square metres.  (2 marks)

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\( 500\ 000\ 000\ \text{m}^{2}\)

Show Worked Solution
\(\text{Area}\) \(= 500 \times 1\ 000\ 000\)  
  \(= 500\ 000\ 000\ \text{m}^{2}\)  

Area, SM-Bank 091

A walled city has a land area of 950 hectares.

Express the area of the city in square kilometres.  (2 marks)

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\(9.5\ \text{km}^2\)

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\(\text{1 hectare}\ = 10\ 000\ \text{m}^{2}\)

\(\text{950 hectares}\ = 950 \times 10\ 000 = 9\ 500\ 000\ \text{m}^{2} \)

\(\text{1 km}^{2}\ = 1000\ \text{m} \times 1000\ \text{m}\ = 1\ 000\ 000\ \text{m}^{2}\)

\(\text{950 hectares}\ = \dfrac{9\ 500\ 000}{1\ 000\ 000} = 9.5\ \text{km}^{2} \)

Area, SM-Bank 088

Convert an area of 9 300 000 square metres into square kilometres.  (1 mark)

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\(9.3\ \text{km}^2\)

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\(\text{1 km}^{2} =1000\ \text{m}\times 1000\ \text{m}\ =1\ 000\ 000\ \text{m}^2\)

\(\text{9 300 000 m}^{2} =\dfrac{9\ 300\ 000}{1\ 000\ 000}=9.3\ \text{km}^2\)

Area, SM-Bank 085

A remote island has a land area of 4.6 square kilometres.

Convert this area into square metres.  (1 mark)

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\(4\ 600\ 000\ \text{m}^2\)

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\( \text{1 km}^{2}\ =1000\ \text{m} \times 1000\ \text{m} = 1\ 000\ 000\ \text{m}^2 \)

\(\text{4.6 km}^{2}\ = 4.6\times 1\ 000\ 000=4\ 600\ 000\ \text{m}^2 \)