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Area, SM-Bank 154

The entrance to a tunnel, pictured below, is a semi-circle with an area of \(28.88\pi \) square metres.
 

Calculate the diameter of the tunnel.  (2 marks)

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\(7.6\ \text{m}\)

Show Worked Solution

\(\text{Area of full circle}\ =2 \times 28.88\pi = 57.76\pi \ \text{m}^{2}\)

\(A\) \(=\pi r^{2} \)
\(57.76 \pi\) \(= \pi r^2\)
\(r^{2}\) \(=57.76\)
\(r\) \(=\sqrt{57.76}\)
  \(=7.6\ \text{m}\)