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Area, SM-Bank 034

The radius of a circle is 6.5 centimetres.

A square has the same area as this circle.

Calculate the side length of the square, in centimetres correct to one decimal place.   (3 marks)

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\(11.5\ \text{cm}\)

Show Worked Solution
\(\text{Area of circle}\) \(=\pi r^2\)
  \(=\pi\times 6.5^2\)
  \(= 132.73\dots\ \text{cm}^2\)

 
\(\text{Area of square}\ =s^2=\ \text{Area of circle}\)

\(s^2\) \(= 132.73\dots\)
\(s\) \(=\sqrt{132.73\dots}\)
  \(= 11.5\ \text{cm (1 d.p.)}\)