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Area, SM-Bank 156

The semi-circle, pictured below, has an area of 32 square centimetres.
 

Calculate the diameter of the semi-circle, giving your answer to 2 decimal places.  (2 marks)

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\(9.03\ \text{cm}\)

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\(\text{Area of full circle}\ =2 \times 32 = 64 \ \text{cm}^{2}\)

\(A\) \(=\pi r^{2} \)
\(64\) \(= \pi r^2\)
\(r^{2}\) \(=\dfrac{64}{\pi} \)
\(r\) \(=\sqrt{20.3718…}\)
  \(=4.5135…\ \text{cm} \)

 
\(\therefore\ \text{Diameter}\ = 2 \times 4.513 = 9.03\ \text{cm (2 d.p.)} \)