Mensuration Structured Questions | Cambridge O Level Mathematics (Syllabus D)

Question 1 of 5 · 9 marks

Mensuration · 3 - Garden Window Sector & Segment

4 parts

Mathematics (Syllabus D) 4024 · Question 1Paper 2 · Calculator[9 marks]

The diagram shows a decorative stained-glass window panel in the shape of a sector $OAB$ of a circle with centre $O$ and radius $15\,\mathrm{cm}$ . The central angle $AOB = 120^\circ$ .

(a)

Calculate the arc length $AB$ , giving your answer to $3$ significant figures.

[2]

(b)

Show that the area of triangle $OAB$ is $\frac{225\sqrt{3}}{4}\,\mathrm{cm}^2 \approx 97.4\,\mathrm{cm}^2$ .

[2]

(c)

Calculate the area of the minor segment bounded by chord $AB$ and arc $AB$ , giving your answer to $3$ significant figures.

[3]

(d)

Calculate the total perimeter of the minor segment, correct to $3$ significant figures.

[2]