Maths · Mensuration · chapter 11 of 14
Class 10 Maths Chapter 11: Areas Related to Circles case study question with answers
One case-based question of the kind the board asks in Section E: a passage and a figure, then 3 parts worth 4 marks in all, with the answer and the marking scheme for each. Written from the NCERT chapter.
Case study · 4 marks
A furniture workshop in Saharanpur makes a round table top of radius 42 cm with centre O. A craftsman sets a stone mosaic into one sector whose two radii are perpendicular, and edges its curved side with a brass strip. Across the opposite side of the top he lays a straight brass inlay AB with ∠AOB = 60°, and the minor segment cut off by AB is stained dark. The mosaic sector and the stained segment are shaded in the figure. Take π = 22/7 and √3 = 1.73.
Part 1 · 1 mark
The length of the brass strip along the curved side of the mosaic is
Show answer
Answer: (b) 66 cm
Arc = (90/360) × 2 × (22/7) × 42 = 66 cm. 1386 is the mosaic's area.
Part 2 · 1 mark
The area of triangle OAB is
Show answer
Answer: (c) 441√3 cm²
OA = OB and ∠AOB = 60°, so the triangle is equilateral of side 42: (√3/4) × 42² = 441√3 cm².
Part 3 · 2 marks
Find the area of the stained segment.
Answer and marking scheme
Sector OAB = (60/360) × (22/7) × 42² = 924 cm². Triangle = 441√3 = 441 × 1.73 = 762.93 cm². Segment = 924 − 762.93 = 161.07 cm².
- sector 924 cm² and triangle 762.93 cm² (1)
- segment 161.07 cm² (1)
Or
Find the area of the table top that is neither mosaic nor stained.
Answer and marking scheme
Top = (22/7) × 42² = 5544 cm². Mosaic = ¼ × 5544 = 1386 cm². Stained segment = 924 − 762.93 = 161.07 cm². Plain part = 5544 − 1386 − 161.07 = 3996.93 cm².
- top 5544 cm², mosaic 1386 cm² and segment 161.07 cm² (1)
- plain part 3996.93 cm² (1)
← Chapter 10: CirclesChapter 12: Surface Areas and Volumes →