Worksheets · Foundation and Higher

Circle vocabulary and perimeter

3 exam-style questions. Answers and the mark for each step are on the last page.

Question 1Non-calculator · 1 mark
(a) A region inside a circle is bounded by one chord and the shorter arc joining the ends of the chord. What is this region called? (1)
1. Sector
2. Tangent
3. Segment
4. Diameter
Question 2Non-calculator · 4 marks
A semicircular window has radius 4 cm. Its border includes the straight diameter.
(a) Find the exact length of the whole border. (3)
(b) Explain why a diameter is also a chord. (1)
Question 3Calculator · 5 marks
A running track has two straight sections, each 80 m long, joined by two semicircular ends with the same radius $r$ metres. The length of the track is 400 m.
(a) Work out the value of $r$ . Give your answer correct to 3 significant figures. (3)
(b) A lane nearer the inside of the curves has semicircles of radius $(r - 1.2)$ m and the same straights. How much shorter is one lap of this lane? Give your answer correct to 3 significant figures. (2)

Answers and marks

(a) Segment

(a) $4\pi +8$

(b) A chord joins two points on the circumference. A diameter does this and also passes through the centre.

C1 Correct conclusion with supporting reasoning: A chord joins two points on the circumference. A diameter does this and also passes through the centre.

(a) $r = 38.2$ m

(b) 7.54 m

Circle vocabulary and perimeter

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