Area, SM-Bank 157

An Aussie Rules football team has booked half of the SCG for a training session. The field available to them under this booking covers 8257 square metres.

Assuming the SCG is perfectly round, determine its diameter, giving your answer in metres to 1 decimal place. (2 marks)

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\(145.0\ \text{m}\)

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\(\text{Area of full SCG}\ =2 \times 8257 = 16\ 514 \ \text{m}^{2}\)

\(A\)	\(=\pi r^{2} \)
\(16\ 514\)	\(= \pi r^2\)
\(r^{2}\)	\(=\dfrac{16\ 514}{\pi} \)
\(r\)	\(=\sqrt{5256.569…}\)
	\(=72.5022…\ \text{m} \)

\(\therefore\ \text{Diameter}\ = 2 \times 72.502 = 145.0\ \text{m (1 d.p.)} \)