What is the diameter of a circle of area 77cm2 [Take \(\pi = \frac{22}{7}\)]

  • A \(\frac{\sqrt{2}}{7}cm\)
  • B \(3\frac{1}{2}cm\)
  • C 7cm
  • D \(7\sqrt{2}cm\)
waec 2005mathematics

The correct answer is D. \(7\sqrt{2}cm\)

\(A=\pi r^2 \Rightarrow 77 = \frac{22}{7} \times \frac{r^2}{1}\Rightarrow r^2 = \frac{77\times 7}{22} \Rightarrow r^2 = \frac{49}{2}\\

\Rightarrow r = \sqrt{\frac{49}{2}}=\frac{7}{\sqrt{2}}. Since D = 2r ∴ D = 2 \times \frac{7}{\sqrt{2}} = \frac{14}{\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}} = 7\sqrt{2}cm\)

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