Areas Related to Circles — Questions & Answers

Sample questions from Areas Related to Circles

1. Q1. In the given figure, a horse is tied at one corner of a square field by a rope 7 m long. The area of the field it can graze is (take π = 22/7):

   • A.154 m²
   • B.38.5 m²✓
   • C.77 m²
   • D.49 m²
   Solution

   At a corner the angle available is 90°, so the grazed region is a quadrant of radius 7 m: 154/4 = 38.5 m².

2. Q2. If the area of a circle is 100π cm², its radius is:

   • A.10 cm✓
   • B.20 cm
   • C.5 cm
   • D.100 cm
   Solution

   πr²=100π gives r=10 cm.

3. Q3. The area of a sector of angle 60° of a circle of radius 6 cm is:

   • A.6π cm²✓
   • B.3π cm²
   • C.12π cm²
   • D.36π cm²
   Solution

   Area of a sector = (θ/360°) × πr² = (60/360) × π × 36 = 6π cm². Option D is the area of the whole circle, and option C comes from using the sector's arc length formula by mistake.

4. Q4. Why does a wheel’s distance per revolution equal its circumference?

   • A.A point on the rim travels one complete circular boundary✓
   • B.It travels the area
   • C.It travels the radius only
   • D.It does not move
   Solution

   One revolution traces the full circumference.

5. Q5. The largest circle that can be drawn inside a square of side 28 cm has area, with π as 22/7:

   • A.784 cm²
   • B.2464 cm²
   • C.616 cm²✓
   • D.308 cm²
   Solution

   C is correct. The largest such circle touches all four sides, so its diameter is 28 cm and its radius 14 cm, giving an area of (22/7)(196) = 616 cm². A gives the area of the square. B takes 28 as the radius rather than the diameter. D halves the correct answer.

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