A stationery order includes circular notepads bound at a central spiral. A quarter of each page, radius \(6\) cm from the spiral, is perforated so it can be...
Question 1 Report
A stationery order includes circular notepads bound at a central spiral. A quarter of each page, radius \(6\) cm from the spiral, is perforated so it can be torn off as a reminder tab, as shown. Work out the area of one tear-off tab, leaving your answer in terms of \(\pi\). (3)
Answer Details
A tear-off tab covering a quarter of the page is a sector whose angle, \(90^\circ\), is exactly one quarter of the full \(360^\circ\), so its area is exactly one quarter of the full circle's area.
\[ \text{area} = \frac{90}{360}\times\pi\times6^2 \] [2 marks]
\[ = 9\pi \text{ cm}^2 \] [1 mark]
Since \(\frac{90}{360}=\frac{1}{4}\) exactly, the tab's area is precisely a quarter of the full page's area, \(\pi\times6^2=36\pi\); leaving the answer as \(9\pi\), as asked, keeps this exact value rather than rounding it to a decimal.
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