Areas Related to Circles

This chapter has

Areas Related to Circles — solved practice questions

8 Class 10 Mathematics questions with step-by-step solutions. Attempt each, then reveal the answer.

1. Q1easy

   The area of a circle with radius r is:

   • A2πr
   • Bπr²
   • Cπr
   • D2πr²
   Show answer & solution

   Correct answer: (B) πr²

   Area = πr².

2. Q2easy

   The circumference of a circle with radius r is:

   • A2πr
   • Bπr²
   • Cπd
   • D2πd
   Show answer & solution

   Correct answer: (A) 2πr

   Circumference = 2πr.

3. Q3medium

   The area of a sector with radius r and angle θ (in degrees) is:

   • A(θ/180)×πr²
   • B(θ/360)×πr
   • C(θ/360)×πr²
   • D(θ/180)×r²
   Show answer & solution

   Correct answer: (C) (θ/360)×πr²

   Area of sector = (θ/360) × πr².

4. Q4medium

   The length of an arc of a sector with radius r and angle θ° is:

   • A(θ/360)×2πr
   • B(θ/180)×πr
   • C(θ/360)×πr²
   • D2πr/θ
   Show answer & solution

   Correct answer: (A) (θ/360)×2πr

   Arc length = (θ/360) × 2πr.

5. Q5easy

   The area of a circle of diameter 14 cm is (use π = 22/7):

   • A44 cm²
   • B154 cm²
   • C196 cm²
   • D308 cm²
   Show answer & solution

   Correct answer: (B) 154 cm²

   r = 7. Area = (22/7)×49 = 154 cm².

6. Q6medium

   A sector has radius 7 cm and angle 90°. Its area is (π = 22/7):

   • A154 cm²
   • B77 cm²
   • C38.5 cm²
   • D19.25 cm²
   Show answer & solution

   Correct answer: (C) 38.5 cm²

   (90/360)×(22/7)×49 = ¼ × 154 = 38.5 cm².

7. Q7medium

   The area of the minor segment is obtained by:

   • AArea of sector + triangle
   • BArea of sector − triangle
   • CArea of circle − sector
   • DArea of circle + triangle
   Show answer & solution

   Correct answer: (B) Area of sector − triangle

   Area of minor segment = Area of sector − Area of triangle (formed by the two radii and chord).

8. Q8medium

   A horse is tied to a pole with a rope 7 m long. The area it can graze is (π = 22/7):

   • A44 m²
   • B77 m²
   • C154 m²
   • D308 m²
   Show answer & solution

   Correct answer: (C) 154 m²

   Area = πr² = (22/7)×49 = 154 m².

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