Areas Related to Circles — Class 10 MCQs with Answers

Areas Related to Circles — important questions & MCQs with answers (Class 10 Mathematics)

14 solved questions from this chapter's difficulty levels, each with its answer and explanation. The other 76 are timed and scored when you sign in.

1. Q1Easy

   Circumference of a circle of radius r:

   A.πr²

   B.2πr✓ Correct

   C.πr

   D.4πr

   Answer: B. 2πr

   Explanation: Circumference = 2πr, the perimeter formula for a circle — don't confuse it with area = πr², which grows with r² not r.

2. Q2Easy

   Area of a circle of radius r is:

   A.πr

   B.2πr

   C.πr²✓ Correct

   D.πd

   Answer: C. πr²

   Explanation: Area = πr² — the radius is squared, unlike circumference (2πr) which is linear in r, a common mix-up between the two formulas.

3. Q3Easy

   Circumference of a circle of radius r is:

   A.πd²

   B.πr²

   C.πr

   D.2πr✓ Correct

   Answer: D. 2πr

   Explanation: Circumference = 2πr, linear in radius — easy to confuse with area (πr²), where r is squared instead.

4. Q4Easy

   Area of a sector of angle θ° in a circle of radius r is:

   A.πr²/360

   B.(θ/360) × πr²✓ Correct

   C.(θ/180)πr

   D.2πr × θ

   Answer: B. (θ/360) × πr²

   Explanation: Sector area = (θ/360) × πr² — the fraction θ/360 scales the full circle's area down to just that wedge.

5. Q5Easy

   Area of a ring (annulus) with outer radius R and inner radius r is:

   A.π(R + r)

   B.πR² + πr²

   C.π(R² − r²)✓ Correct

   D.π(R − r)²

   Answer: C. π(R² − r²)

   Explanation: Ring area = π(R² − r²) — subtract the inner circle's area from the outer circle's, not (R−r)² which is a different, smaller expression entirely.

6. Q6Easy

   Area of a circle with r = 7 cm (π=22/7):

   A.154 cm²✓ Correct

   B.49 cm²

   C.44 cm²

   D.22 cm²

   Answer: A. 154 cm²

   Explanation: Area = πr² = (22/7) × 7² = (22/7) × 49 = 154 cm² — squaring the radius first avoids the common slip of using 2πr (circumference) instead.

7. Q7Medium

   Taking π = 22/7, a wheel of diameter 84 cm makes 100 complete revolutions. The distance covered is:

   A.132 m

   B.264 m✓ Correct

   C.528 m

   D.26.4 m

   Answer: B. 264 m

   Explanation: One revolution covers (22/7)(84) = 264 cm, so 100 revolutions cover 26400 cm = 264 m.

8. Q8Medium

   If the area of a circle is 314 cm² (π = 3.14), its diameter is:

   A.100 cm

   B.10 cm

   C.20 cm✓ Correct

   D.31.4 cm

   Answer: C. 20 cm

   Explanation: From Area = πr²: r² = 314 ÷ 3.14 = 100, so r = 10 cm and diameter = 20 cm — don't forget to double the radius for diameter.

9. Q9Medium

   Area of sector of radius 7, angle 90°:

   A.77 cm²

   B.154/4 = 38.5 cm²✓ Correct

   C.49 cm²

   D.22 cm²

   Answer: B. 154/4 = 38.5 cm²

   Explanation: Sector area = (θ/360) × πr² = (90/360) × (22/7×49) = (1/4)×154 = 38.5 cm² — a quarter of the full circle's area since 90° is a quarter turn.

10. Q10Medium

    A wheel has diameter 70 cm. Distance covered in 100 revolutions (π = 22/7):

    A.100 m

    B.220 m✓ Correct

    C.440 m

    D.700 m

    Answer: B. 220 m

    Explanation: Circumference = πd = (22/7)×70 = 220 cm per revolution; 100 revolutions cover 100×220 = 22,000 cm = 220 m.

11. Q11Medium

    Area of a minor segment of a circle of radius 10 cm with chord subtending 90° at centre (π = 3.14):

    A.57 cm²

    B.78.5 cm²

    C.28.5 cm²✓ Correct

    D.50 cm²

    Answer: C. 28.5 cm²

    Explanation: Segment = sector − triangle: sector area = (90/360)×π×10² = 25π = 78.5 cm²; triangle (right angle at centre) = (1/2)×10×10 = 50 cm²; segment = 78.5 − 50 = 28.5 cm².

12. Q12Hard

    If perimeter of a semicircle is 36 cm (π=22/7), radius =

    A.21 cm

    B.14 cm

    C.7 cm✓ Correct

    D.5 cm

    Answer: C. 7 cm

    Explanation: Perimeter of a semicircle = πr + 2r = r(π+2). Setting r×(22/7+2) = r×36/7 = 36 gives r = 7 cm — remember to add the straight diameter edge, not just the arc.

13. Q13Hard

    The areas of two circles are in the ratio 25 : 16. Ratio of their circumferences:

    A.5 : 4✓ Correct

    B.25 : 16

    C.4 : 5

    D.2 : 1

    Answer: A. 5 : 4

    Explanation: Area ∝ r², so (r₁/r₂)² = 25/16 gives r₁/r₂ = 5/4; since circumference ∝ r linearly, the circumference ratio equals the same 5:4.

14. Q14Hard

    Area of minor segment = area of sector − area of:

    A.Rectangle

    B.Square

    C.Circle

    D.Triangle✓ Correct

    Answer: D. Triangle

    Explanation: The chord and the two radii form a triangle; subtracting its area from the sector's area removes the straight-edged piece, leaving the curved minor segment.

Areas Related to Circles — FAQs

More Class 10 Mathematics chapters

• 01Real Numbers
• 02Polynomials
• 03Pair of Linear Equations in Two Variables
• 04Quadratic Equations
• 05Arithmetic Progressions
• 06Triangles

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