Exercise 12.1 5 Questions – Areas & Perimeters of Circles
The radii of two circles are 19 cm and 9 cm respectively. Find the radius of the circle which has circumference equal to the sum of the circumferences of the two circles.
C₁ = 2π—19 = 38π. C₂ = 2π—9 = 18π. Total = 56π. For new circle: 2πR = 56π ' R = 28 cm
Q3: A car has two wipers which do not overlap. Each wiper has blade of 25 cm sweeping 115°. Find total area cleaned at each sweep. ' Area = 2 — (115/360)π(25)² = 2—115/360—3.14—625 ≈ 1254 cm²
Q4: Find area of circle with same area as sum of areas of circles of radii 10 cm, 12 cm, 24 cm. ' A=π(100+144+576)=820π. R=√820=2√205 cm
Exercise 12.2 14 Questions – Sectors & Segments
Find area of sector of circle with radius 6 cm if angle of sector is 60°. (π=22/7)
Area = (60/360) — π — 6² = (1/6) — (22/7) — 36 = (22—36)/(7—6) = 132/7 ≈ 18.86 cm²
Q4: A chord of a circle of radius 10 cm subtends a right angle at the centre. Find: (i) area of minor segment (ii) area of major sector.
Minor segment = (90/360)π(100) ' ½(10—10) = 25π ' 50 = 25(π'2) ≈ 28.5 cm². Major sector = (270/360)π(100) = 75π = 235.5 cm²
Q6: Chord of radius 15 cm subtending 60°: find areas of minor and major segments. Minor segment = (60/360)π(225) ' (√3/4)(225) = 37.5π ' 56.25√3 = 20.44 cm². Major segment = π(225) ' 20.44 = 686.06 cm²
Q8: A horse tied to a peg at one corner of square 30 m grass field with 5 m rope. Area grazed? ' (90/360)π(5)² = 19.64 m²
Q10: Umbrella has 8 ribs equally spaced. If umbrella is 45 cm flat circle, area between two consecutive ribs. ' (360/8)/360 — π(45)² = (1/8)π(2025) = 795.5 cm²
Q14: Minute hand of clock is 14 cm long. Area swept in 5 minutes. ' (30/360)π(14)² = (1/12)π(196) = 51.33 cm²
Exercise 12.3 16 Questions – Combinations of Plane Figures
Q2: Find area of shaded region where radii of two concentric circles are 7 cm and 14 cm and ∠AOC=40°. ' Shaded = sector(big) ' sector(small) = (40/360)π(14²'7²) = (1/9)(22/7)(196'49) = (1/9)(22/7)(147) = 51.33 cm²
Q4: Find area of shaded design in square ABCD of side 10 cm where semicircles are drawn on each side. ' Area = 100 + 2π(5)² ' 100 = 2—25π'100 = 50π'100 ≈ 57 cm²
Q6: Circular table cover of radius 32 cm has design forming equilateral "ABC in middle. Find area of design. ' "ABC has side = 32√3. Area = (√3/4)(32√3)² = (√3/4)(3072) = 768√3 ≈ 1330.18 cm²
Q10: An archery target has 5 scoring regions formed by concentric circles with radii increasing by 3.5 cm. Find area of black region (5th from centre). ' Black = π(17.5²'14²) = π(306.25'196) = 110.25π ≈ 346.5 cm²
Q14: Flower bed is in shape of quadrant of circle of radius 1 m. Two semicircles are drawn on two sides touching the quarter circle. Find area of flower bed. ' Area ≈ 0.57 m²
Q16: Calculate area of designed region common between two quadrants of circles of radius 8 cm each. ' 36.57 cm²
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