Question
Question: A running track is formed of a rectangle 80 m by 50 m with a semicircle attached to each of the shorter (50 m) ends. Calculate (a) the total perimeter and (b) the total enclosed area. Give answers to 1 d.p.
Mark scheme (5 marks):
- M1: Recognise the two semicircles together form a full circle of diameter 50 m, so radius r = 25 m.
- (a) M1: Perimeter = 2 × 80 + circumference = 160 + 2π(25) = 160 + 50π
- A1: Perimeter = 317.1 m (1 d.p.)
- (b) M1: Area = rectangle + circle = (80 × 50) + π(25)² = 4000 + 625π
- A1: Area = 5963.5 m² (1 d.p.)
Accept 5963.4 m² if 625π evaluated as 1963.495....
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Generated by TopMyGrade AI · cross-check official sources before relying on the mark-scheme phrasing.