Moderate -0.3 This is a standard segment area question requiring the formula (½r²θ - ½r²sinθ) with values directly given. It's slightly easier than average because it's a direct application of a bookwork formula with no problem-solving required, though students must remember to subtract the triangle area from the sector area.
\includegraphics{figure_6}
A circle with centre O has radius \(12.4\) cm. A segment of the circle is shown shaded in Fig. 6. The segment is bounded by the arc AB and the chord AB, where the angle AOB is \(2.1\) radians. Calculate the area of the segment. [4]
or \(\pi \times \frac{120.32}{360} \times 12.4^2\); angle in degrees to 3 sf or better
\(\frac{1}{2} \times 12.4^2 \times \sin2.1 (= 66.3 \text{ to } 66.4)\) or \(\frac{1}{2} \times 21.5(121\ldots) \times 6.16(9\ldots)\)
M1*
angle in degrees to 3 sf or better; may be implied by \(2.81(7168325\ldots)\) (degrees) or \(2.53(5559362)\) (grad)
their \(161.448 -\) their \(66.36\)
M1dep*
if unsupported, B4 for \(95.08(446)\) r.o.t. to 4 sf or better
\(95\) to \(95.1\)
A1
Total: [4]
$\frac{1}{2} \times 12.4^2 \times 2.1 (= 161.448)$ | M1* | or $\pi \times \frac{120.32}{360} \times 12.4^2$; angle in degrees to 3 sf or better
$\frac{1}{2} \times 12.4^2 \times \sin2.1 (= 66.3 \text{ to } 66.4)$ or $\frac{1}{2} \times 21.5(121\ldots) \times 6.16(9\ldots)$ | M1* | angle in degrees to 3 sf or better; may be implied by $2.81(7168325\ldots)$ (degrees) or $2.53(5559362)$ (grad)
their $161.448 -$ their $66.36$ | M1dep* | if unsupported, B4 for $95.08(446)$ r.o.t. to 4 sf or better
$95$ to $95.1$ | A1 |
**Total: [4]**
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\includegraphics{figure_6}
A circle with centre O has radius $12.4$ cm. A segment of the circle is shown shaded in Fig. 6. The segment is bounded by the arc AB and the chord AB, where the angle AOB is $2.1$ radians. Calculate the area of the segment. [4]
\hfill \mbox{\textit{OCR MEI C2 2014 Q6 [4]}}