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.
Câ‚ = 2π×19 = 38Ï€. Câ‚‚ = 2π×9 = 18Ï€. Total = 56Ï€. For new circle: 2Ï€R = 56Ï€ â‡' 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. â†' Area = 2 × (115/360)Ï€(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. â†' A=Ï€(100+144+576)=820Ï€. 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)Ï€(100) âˆ' ½(10×10) = 25Ï€ âˆ' 50 = 25(Ï€âˆ'2) ≈ 28.5 cm². Major sector = (270/360)Ï€(100) = 75Ï€ = 235.5 cm²
Q6: Chord of radius 15 cm subtending 60°: find areas of minor and major segments. Minor segment = (60/360)Ï€(225) âˆ' (√3/4)(225) = 37.5Ï€ âˆ' 56.25√3 = 20.44 cm². Major segment = Ï€(225) âˆ' 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? â†' (90/360)Ï€(5)² = 19.64 m²
Q10: Umbrella has 8 ribs equally spaced. If umbrella is 45 cm flat circle, area between two consecutive ribs. â†' (360/8)/360 × Ï€(45)² = (1/8)Ï€(2025) = 795.5 cm²
Q14: Minute hand of clock is 14 cm long. Area swept in 5 minutes. â†' (30/360)Ï€(14)² = (1/12)Ï€(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°. â†' Shaded = sector(big) âˆ' sector(small) = (40/360)Ï€(14²âˆ'7²) = (1/9)(22/7)(196âˆ'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. â†' Area = 100 + 2Ï€(5)² âˆ' 100 = 2×25Ï€âˆ'100 = 50Ï€âˆ'100 ≈ 57 cm²
Q6: Circular table cover of radius 32 cm has design forming equilateral Î"ABC in middle. Find area of design. â†' Î"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). â†' Black = Ï€(17.5²âˆ'14²) = Ï€(306.25âˆ'196) = 110.25Ï€ ≈ 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. â†' Area ≈ 0.57 m²
Q16: Calculate area of designed region common between two quadrants of circles of radius 8 cm each. â†' 36.57 cm²
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