11. Areas Related to Circles

*नोट: यह सेक्शन रिवीजन के लिए है। अपना ज्ञान परखने के लिए ऊपर दिए गए क्विज़ में भाग लें।

1. What is the exact mathematical formula to calculate the circumference of a circle with radius r?
   A) pi * r^2  |  B) 2 * pi * r  |  C) pi * r  |  D) 4 * pi * r
2. The exact mathematical area of a circle with radius r is given strictly by which formula?
   A) 2 * pi * r  |  B) pi * r^2  |  C) 2 * pi * r^2  |  D) pi * d
3. If the specific angle of a sector is exactly theta degrees, what is the precise formula for the area of the sector?
   A) (theta / 180) * pi * r^2  |  B) (theta / 360) * 2 * pi * r  |  C) (theta / 360) * pi * r^2  |  D) (theta / 90) * pi * r^2
4. What is the exact mathematical formula for the length of an arc of a sector with an angle of precisely theta degrees?
   A) (theta / 360) * 2 * pi * r  |  B) (theta / 180) * pi * r  |  C) (theta / 360) * pi * r^2  |  D) (theta / 90) * 2 * pi * r
5. The total angle mathematically subtended perfectly at the exact center of a complete circle is precisely:
   A) 90 degrees  |  B) 180 degrees  |  C) 270 degrees  |  D) 360 degrees
6. A specific region perfectly enclosed strictly between a straight chord and its corresponding circular arc is mathematically called:
   A) Sector  |  B) Segment  |  C) Radius  |  D) Diameter
7. The exact mathematical perimeter of a perfect semicircle with radius r strictly equals:
   A) pi * r  |  B) pi * r + 2r  |  C) 2 * pi * r  |  D) pi * r^2
8. If exactly the numerical area of a circle is numerically perfectly equal to its precise circumference, what is the exact numerical radius?
   A) 1 unit  |  B) 2 units  |  C) pi units  |  D) 4 units
9. The exact area of a perfect quadrant of a complete circle with specific radius r mathematically equals:
   A) (1/2) * pi * r^2  |  B) (1/3) * pi * r^2  |  C) (1/4) * pi * r^2  |  D) (1/6) * pi * r^2
10. What is the precise mathematical ratio of the exact circumference of a geometric circle strictly to its complete diameter?
    A) r  |  B) pi  |  C) 2 * pi  |  D) pi / 2
11. Calculate the exact mathematical area of a geometric sector perfectly with radius exactly 6 cm and central angle precisely 60 degrees.
    A) 6 * pi cm^2  |  B) 12 * pi cm^2  |  C) 36 * pi cm^2  |  D) 3 * pi cm^2
12. If the exact radius of a geometric circle is perfectly mathematically doubled, exactly how many times does its precise numerical area increase?
    A) 2 times  |  B) 3 times  |  C) 4 times  |  D) 8 times
13. A mechanical clock minute hand strictly 14 cm long perfectly describes what exact mathematical area exactly in 5 minutes?
    A) 51.33 cm^2  |  B) 154 cm^2  |  C) 102.66 cm^2  |  D) 77 cm^2
14. What specific angle is perfectly mathematically described strictly by the minute hand of a clock exactly in 1 minute?
    A) 1 degree  |  B) 5 degrees  |  C) 6 degrees  |  D) 10 degrees
15. The exact numerical difference mathematically strictly between the precise circumference and radius of a specific circle is exactly 37 cm. Find the precise radius.
    A) 7 cm  |  B) 14 cm  |  C) 21 cm  |  D) 28 cm
16. A perfectly circular spinning wheel directly mathematically covers a strict distance of exactly 88 km perfectly in 1000 complete revolutions. The exact radius is:
    A) 7 m  |  B) 14 m  |  C) 21 m  |  D) 28 m
17. Find the precise geometric area of a perfectly mathematically defined quadrant exactly of a circle strictly having a perfect circumference of exactly 22 cm.
    A) 77/2 cm^2  |  B) 77/4 cm^2  |  C) 77/8 cm^2  |  D) 77/16 cm^2
18. The exact mathematical ratio of the completely distinct numerical areas strictly of 2 specific circles is exactly 16:25. The precise mathematical ratio strictly of their geometric circumferences is:
    A) 16:25  |  B) 4:5  |  C) 256:625  |  D) 2:3
19. If strictly the geometric perimeters precisely of a circle and a perfect square are mathematically completely equal, what is the exact ratio of their areas?
    A) 14:11  |  B) 11:14  |  C) 22:7  |  D) 7:22
20. The exact mathematical numerical length of a perfect circular arc precisely subtending a geometric angle of exactly 90 degrees perfectly at the center specifically of radius exactly 14 cm is:
    A) 11 cm  |  B) 22 cm  |  C) 33 cm  |  D) 44 cm
21. Calculate the exact area of the perfectly mathematical minor segment precisely of a circle exactly of radius strictly 14 cm when the central geometric angle is exactly 90 degrees.
    A) 56 cm^2  |  B) 154 cm^2  |  C) 98 cm^2  |  D) 200 cm^2
22. The perfectly straight geometric chord mathematically of a specific circle strictly of exact radius precisely 12 cm subtends exactly an angle perfectly of 120 degrees directly at the center. Find the precise segment area.
    A) (48 * pi - 36 * sqrt(3)) cm^2  |  B) (24 * pi - 36 * sqrt(3)) cm^2  |  C) (48 * pi - 18 * sqrt(3)) cm^2  |  D) (24 * pi - 18 * sqrt(3)) cm^2
23. What is the exact calculated geometric area perfectly of the absolute largest completely perfect square that can be rigorously inscribed mathematically strictly inside a perfect circle specifically of exact radius r?
    A) r^2  |  B) 2 * r^2  |  C) sqrt(2) * r^2  |  D) 4 * r^2
24. If exactly the numerical calculated area strictly of a perfect geometric circle precisely inscribed mathematically strictly in a perfect square is exactly 9 * pi cm^2, exactly what is the complete square's area?
    A) 18 cm^2  |  B) 24 cm^2  |  C) 36 cm^2  |  D) 81 cm^2
25. Find the precise mathematical geometric area specifically of exactly the complete geometric ring perfectly mathematically formed strictly between 2 totally concentric circles exactly of radii precisely 7 cm and exactly 14 cm.
    A) 154 cm^2  |  B) 308 cm^2  |  C) 462 cm^2  |  D) 616 cm^2
26. A massive strong metallic silver wire is perfectly bent entirely to physically form a completely perfect square mathematically of exact area exactly 121 cm^2. If the completely exact same physical wire is structurally bent precisely into a circle, find its exact area.
    A) 154 cm^2  |  B) 110 cm^2  |  C) 220 cm^2  |  D) 308 cm^2
27. A fast car has exactly 2 perfect identical mechanical wipers perfectly exactly of physical length strictly 25 cm precisely mathematically sweeping completely through a specific geometric angle exactly of 115 degrees. Find the exact total swept area.
    A) 158125/252 cm^2  |  B) 158125/126 cm^2  |  C) 316250/252 cm^2  |  D) 158125/360 cm^2
28. The mathematically precise sum precisely of the exact specific areas strictly of exactly 2 perfect completely separate geometric circles exactly of radii strictly R1 and exactly R2 mathematically perfectly equals the precise specific area entirely of a third circle precisely with specific exact radius R. Which relation is exactly true?
    A) R1 + R2 = R  |  B) R1^2 + R2^2 = R^2  |  C) R1 + R2 < R  |  D) R1^2 + R2^2 > R^2
29. An agricultural circular field clearly correctly precisely has exactly a highly specific calculated complete perimeter mathematically precisely of exactly 110 meters. The perfectly completely strict exact calculated area mathematically precisely of exactly the completely specific agricultural field is:
    A) 962.5 m^2  |  B) 1925 m^2  |  C) 3850 m^2  |  D) 7700 m^2
30. If strictly a purely mathematical specific perfectly geometric arc precisely correctly strictly mathematically clearly forms perfectly precisely exactly a complete mathematically specific exact continuous exact length precisely of exact length clearly 5 * pi cm perfectly specifically directly at a complete angle exactly of strictly 30 degrees, exactly precisely what completely correctly specifically is the perfectly exact geometric radius?
    A) 15 cm  |  B) 30 cm  |  C) 45 cm  |  D) 60 cm