Areas Related to Circles — Chapter Test | Class 10 IMO

Q1

If the central angle is 0°, the area of the sector is:

A 0° sector encloses no area.

Q2

A circular running track has inner radius 21 m and outer radius 28 m. The area of the track (π = 22/7) is:

π(28² − 21²) = (22/7)(784 − 441) = (22/7)(343) = 1078 m².

Q3

A circle and a square have equal perimeters. The figure with the larger area is the:

For a fixed perimeter, the circle encloses the maximum area.

Q4

A semicircle is what fraction of the full circle's area?

A semicircle is half the circle.

Q5

The minute hand of a clock sweeps a full circle in:

The minute hand completes one revolution in 60 minutes.

Q6

The area of a ring between two concentric circles of radii 14 cm and 7 cm (π = 22/7) is:

Area = π(R² − r²) = (22/7)(196 − 49) = (22/7)(147) = 462 cm².

Q7

A wheel of diameter 84 cm makes 100 complete revolutions. The distance covered (π = 22/7) is:

Distance = 100 × πd = 100 × (22/7) × 84 = 26400 cm = 264 m.

Q8

The area of a circle circumscribing a square of side 14 cm (π = 22/7) is:

Diameter = diagonal = 14√2, so r = 7√2 and area = (22/7)(98) = 308 cm².

Q9

The area of a circle of radius 7 cm (π = 22/7) is:

Area = πr² = (22/7) × 49 = 154 cm².

Q10

The area of a semicircle of radius 7 cm (π = 22/7) is:

Area = ½πr² = ½ × 154 = 77 cm².

Q11

The minute hand of a clock is 14 cm long. The area it sweeps in 15 minutes (π = 22/7) is:

15 minutes is a 90° sector: (1/4)(22/7)(196) = 154 cm².

Q12

A pizza of radius 14 cm is cut into 8 equal slices. The area of one slice (π = 22/7) is:

Total area = 616 cm²; one of 8 slices = 616 ÷ 8 = 77 cm².

Q13

The area of a sector of angle 60° in a circle of radius 21 cm (π = 22/7) is:

(60/360) × (22/7) × 441 = (1/6) × 1386 = 231 cm².

Q14

The area of the minor segment of a circle of radius 14 cm cut off by a quarter (90°) sector (π = 22/7) is:

Sector 154 cm² minus the right triangle ½ × 14 × 14 = 98 cm² gives 56 cm².

Q15

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

A quadrant is a 90° sector: (1/4) × (22/7) × 196 = 154 cm².