The diagram shows a quarter circle with radius \(10.6\) cm. Calculate its area. Give your answer correct to 3 significant figures.
Question 1 Report
The diagram shows a quarter circle with radius \(10.6\) cm.
Calculate its area. Give your answer correct to 3 significant figures.
Answer Details
A quarter circle is a sector with an angle of \(90^\circ\) at the centre, and \(90^\circ\) is one quarter of the full \(360^\circ\). Its area is therefore one quarter of the area of the whole circle of the same radius.
\[ A=\frac{\pi r^2}{4}=\frac{\pi\times 10.6^2}{4} \] [M1]
The full circle has area \(\pi\times 112.36=352.989...\) cm\(^2\), so
\[ A=\frac{352.989...}{4}=88.247... \]
Correct to 3 significant figures, the area is \(88.2\) cm\(^2\) [A1] (\(88.247...\) is accepted).
The \(10.6\) cm is the radius of the quarter circle, which is one of its two straight edges. Do not halve it: the straight edges of a quarter circle are radii, not diameters. Also keep the distinction between area and perimeter, since the perimeter would need the arc \(\frac{2\pi\times 10.6}{4}\) plus the two straight edges.
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