A trader at a local market has a sign above her stall. The sign is a semicircle. The straight edge along the bottom of the sign is 1.4 m long. She wants to ...
Question 1 Report
A trader at a local market has a sign above her stall. The sign is a semicircle. The straight edge along the bottom of the sign is 1.4 m long. She wants to paint the front of the sign and fit a strip of trim all the way round its edge.
- Find the area of the front of the sign, correct to 3 significant figures. (2)
- Find the perimeter of the sign, correct to 3 significant figures. (2)
Answer Details
The straight edge along the bottom of a semicircular sign is its diameter, so the radius is half of 1.4 m, that is 0.7 m. Getting that step right is what both parts depend on.
(a) Area of the front of the sign. [2]
A semicircle is half a circle, so
Write the answer as 0.770 rather than 0.77, since three significant figures are required and the trailing zero is one of them.
(b) Perimeter of the sign. [2]
The boundary is the curved edge plus the straight bottom edge. The curved part is half the circumference:
Adding the straight edge:
\[P = 2.1991\ldots + 1.4 = 3.5991\ldots = 3.60\ \text{m (3 s.f.)}\]The commonest error is to give only the arc, forgetting the flat bottom, which is a real edge of the sign and needs trim just as much as the curve does.
Examination point: for any half-shape, halve the area formula but treat the perimeter separately, because cutting a circle in half creates a new straight edge that did not exist before. Half the circumference is not the perimeter of a semicircle.
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