A rectangle is drawn around a sector of a circle as shown. If the angle of the sector is 1 radian and the area of the sector is \(7{\text{ c}}{{\text{m}}^2}\), find the dimensions of the rectangle, giving your answers to the nearest millimetre.

\(\frac{1}{2}{r^2} \times 1 = 7\)     M1

\(r = 3.7 \ldots \left( { = \sqrt {14} } \right)\) (or 37… mm)     (A1)

\({\text{height}} = 2r\cos \left( {\frac{{\pi  - 1}}{2}} \right){\text{ }}\left( {{\text{or }}2r\sin \frac{1}{2}} \right)\)     (M1)(A1)

3.59 or anything that rounds to 3.6     A1

so the dimensions are 3.7 by 3.6 (cm or 37 by 36 mm)     A1

[6 marks]

Most students found the value of \(r\) , but a surprising number had difficulties finding the height of the rectangle by any one of the many methods possible. Those that did, frequently failed to round their final answer to the required accuracy leading to few students obtaining full marks on this question. A surprising number of students found the area – clearly misinterpreting the meaning of “dimensions”.