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Chapter 11: Areas Related to Circles — Online MCQ Test

MATHS · Grade 10 · CBSE(NCERT)
Practice Chapter 11: Areas Related to Circles with a free chapter-wise online MCQ test. This chapter covers: Circle Circumference Sector Segment Arc Length Area of sector Area of segment Composite figures Perimeter. AI-generated questions from basic to board-exam level, with instant results and explanations.

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Chapter 11: Areas Related to Circles — Important Questions & Answers

What is the circumference of a circle of radius r?
  • A. πr
  • B. 2πr
  • C. πr²
  • D. 2πr²
Answer: B. 2πr
The circumference of a circle is given by C = 2πr, where r is the radius.
The area of a circle with diameter d is:
  • A. πd²
  • B. 2πd²
  • C. πd²/4
  • D. πd/2
Answer: C. πd²/4
Radius is d/2, so area = π(d/2)² = πd²/4.
Using π = 22/7, the circumference of a circle of radius 7 cm is:
  • A. 22 cm
  • B. 44 cm
  • C. 49 cm
  • D. 154 cm
Answer: B. 44 cm
Circumference = 2πr = 2 × 22/7 × 7 = 44 cm.
A racing track consists of a rectangle of length 100 m and breadth 50 m with semicircular ends on the breadths. What is its perimeter?
  • A. 200 + 25π m
  • B. 200 + 50π m
  • C. 300 + 50π m
  • D. 100 + 100π m
Answer: B. 200 + 50π m
The two semicircular ends together form one full circle of diameter 50 m. Perimeter = 2 × 100 + π × 50 = 200 + 50π m.
Three goats are tied at the three vertices of an equilateral triangular field of side 14 m, each with a rope of length 7 m. Using π = 22/7, find the area of the field not grazed by the goats.
  • A. 49√3 - 77 m²
  • B. 77 - 49√3 m²
  • C. 49√3 - 154 m²
  • D. 98√3 - 77 m²
Answer: A. 49√3 - 77 m²
Area of triangle = 49√3 m². The grazed area is three 60° sectors of radius 7 m, equal to 77 m²; hence ungrazed area = 49√3 - 77 m².