A price label at a corner shop is cut as a rectangle with a semicircle joined to one short edge, as shown. 14 cm8 cm© EAGLE BEACON GLOBAL Calculate the peri...
Question 1 Report
A price label at a corner shop is cut as a rectangle with a semicircle joined to one short edge, as shown.
Calculate the perimeter of the label. Give your answer correct to 3 significant figures. (3)
Answer Details
The perimeter is the distance all the way round the outside of the label. The right-hand short edge of the rectangle is not part of that outside boundary, because the semicircle is joined there; the dashed line in the figure marks it as an internal join. The boundary is therefore three straight edges plus one semicircular arc.
The semicircle sits on the short edge of \(8\) cm, so that edge is its diameter and the radius is \(4\) cm. The arc is half a full circumference:
\[\text{arc} = \frac{1}{2} \times 2 \times \pi \times 4 = 4\pi\][1]
\[4\pi = 12.566... \text{ cm}\][1]
Adding the two long edges of \(14\) cm and the remaining short edge of \(8\) cm:
\[\text{Perimeter} = 14 + 8 + 14 + 12.566... = 48.566...\]so the perimeter is \(48.6\) cm correct to 3 significant figures. [1]
The two errors that cost marks are including the internal \(8\) cm join as well as the arc, and using \(8\) cm as the radius rather than the diameter. Reading the dashed line as a construction line, not an edge, settles the first.
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