Chapter Exam

Chapter 11: Areas Related to Circles — Online MCQ Test

Q: What is the circumference of a circle of radius r?

Answer: B. 2πr — The circumference of a circle is given by C = 2πr, where r is the radius.

Q: The area of a circle with diameter d is:

Answer: C. πd²/4 — Radius is d/2, so area = π(d/2)² = πd²/4.

Q: The length of an arc of a circle of radius r and central angle θ is:

Answer: A. θ/360 × 2πr — Arc length is the same fraction of the circumference as θ is of 360°.

Q: The area of a sector of angle θ in a circle of radius r is:

Answer: C. θ/360 × πr² — A sector with angle θ occupies θ/360 part of the circle, so its area is θ/360 × πr².

Q: Using π = 22/7, the circumference of a circle of radius 7 cm is:

Answer: B. 44 cm — Circumference = 2πr = 2 × 22/7 × 7 = 44 cm.

Q: Using π = 22/7, find the area of a sector of radius 21 cm and angle 60°.

Answer: A. 231 cm² — Area of sector = 60/360 × 22/7 × 21 × 21 = 231 cm².

Q: 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?

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.

Q: Find the area of the minor segment of a circle of radius 14 cm when the central angle is 60°, using π = 22/7.

Answer: A. 308/3 - 49√3 cm² — Area of sector = 60/360 × 22/7 × 14² = 308/3 cm². The triangle is equilateral with area 49√3 cm², so segment area = 308/3 - 49√3 cm².

Q: 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.

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.

Q: Two equal circles of radius 14 cm have their centres 14 cm apart. Using π = 22/7, find the area common to both circles.

Answer: A. 616/3 - 98√3 cm² — The common region is made of two identical 60° segments. Each segment has area 308/3 - 49√3, so total common area = 616/3 - 98√3 cm².

MATHS · CLASS 10th · Karnataka State Board

Practice Chapter 11: Areas Related to Circles with a free chapter-wise online MCQ test for Karnataka State Board CLASS 10th MATHS. 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 (FAQ)

Frequently asked questions from Karnataka State Board CLASS 10th MATHS — Chapter 11: Areas Related to Circles, with answers and explanations. These are sample questions; the exam has its own separate question set.

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.

The length of an arc of a circle of radius r and central angle θ is:

A. θ/360 × 2πr ✓
B. θ/360 × πr²
C. 360/θ × 2πr
D. θ/180 × πr²

Answer: A. θ/360 × 2πr
Arc length is the same fraction of the circumference as θ is of 360°.

The area of a sector of angle θ in a circle of radius r is:

A. θ/360 × 2πr
B. θ/180 × πr²
C. θ/360 × πr² ✓
D. 360/θ × πr²

Answer: C. θ/360 × πr²
A sector with angle θ occupies θ/360 part of the circle, so its area is θ/360 × πr².

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.

Using π = 22/7, find the area of a sector of radius 21 cm and angle 60°.

A. 231 cm² ✓
B. 462 cm²
C. 693 cm²
D. 1386 cm²

Answer: A. 231 cm²
Area of sector = 60/360 × 22/7 × 21 × 21 = 231 cm².

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.

Find the area of the minor segment of a circle of radius 14 cm when the central angle is 60°, using π = 22/7.

A. 308/3 - 49√3 cm² ✓
B. 308/3 + 49√3 cm²
C. 154 - 49√3 cm²
D. 49√3 - 308/3 cm²

Answer: A. 308/3 - 49√3 cm²
Area of sector = 60/360 × 22/7 × 14² = 308/3 cm². The triangle is equilateral with area 49√3 cm², so segment area = 308/3 - 49√3 cm².

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.

Two equal circles of radius 14 cm have their centres 14 cm apart. Using π = 22/7, find the area common to both circles.

A. 616/3 - 98√3 cm² ✓
B. 308/3 - 49√3 cm²
C. 616/3 + 98√3 cm²
D. 308/3 + 49√3 cm²

Answer: A. 616/3 - 98√3 cm²
The common region is made of two identical 60° segments. Each segment has area 308/3 - 49√3, so total common area = 616/3 - 98√3 cm².

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