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Unit Conversion, SM-Bank 017

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

1 m² = _____ cm  ×  _____ cm = __________ cm²   (1 mark)

  1. A circular elevator has a diameter of 1.6 metres.
  2. Find the area of the elevator's floor in square metres and using the conversion equation, express the area to the nearest square centimetre.  (2 marks)
Show Answers Only

a.    \(1\ \text{m}^{2} = 100\ \text{cm}\ \times\ 100\ \text{cm}\ = 10\ 000\ \text{cm}^{2} \)

b.    \(20\ 106\ \text{cm}^{2}\)

Show Worked Solution

a.    \(1\ \text{m}^{2} = 100\ \text{cm}\ \times\ 100\ \text{cm}\ = 10\ 000\ \text{cm}^{2} \)
 

b.    \(\text{Radius}\ =\dfrac{1.6}{2} = 0.8\ \text{m} \)

\(\text{Area}\) \(=\pi \times 0.8^2\)  
  \(=2.01061…\ \text{m}^{2}\)  
  \(=2.01061… \times 10\ 000\ \text{cm}^{2}\)  
  \(=20\ 106\ \text{cm}^{2}\)