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පසුගිය ප්‍රශ්න පත්‍ර පුහුණුව

විසඳුම් සහිතව පරිමිතිය පිළිබඳ සා/පෙළ විභාග ප්‍රශ්න පුහුණු වන්න

1. A sector of a circle has radius 21 cm and centre angle 120°. Using π = 22/7, find (i) the arc length of the sector, (ii) the perimeter of the sector.
   විසඳුම බලන්න

   (i) Arc length = (θ/360) × 2πr = (120/360) × 2 × (22/7) × 21. Simplify 120/360 = 1/3, and cancel 21/7 = 3: arc = (1/3) × 2 × 22 × 3 = 44 cm. (ii) Perimeter = arc + 2r = 44 + 2 × 21 = 44 + 42 = 86 cm.
   ආදර්ශයට ගත්තේ: modelled on the MATHEMATICS OL_10 exam pattern
2. A quadrant-shaped garden plot has a radius of 28 m. A fence is to be built along the entire boundary of the plot. Using π = 22/7, calculate the total length of fencing required.
   විසඳුම බලන්න

   A quadrant has centre angle 90°. Arc length = (90/360) × 2πr = (1/4) × 2 × (22/7) × 28 = (1/4) × 176 = 44 m. The two straight sides are radii, so their total length = 2 × 28 = 56 m. Total perimeter = 44 + 56 = 100 m. Therefore, 100 m of fencing is needed.
   ආදර්ශයට ගත්තේ: modelled on the MATHEMATICS OL_10 exam pattern
3. A compound shape is formed by joining a rectangle of length 20 cm and width 14 cm to a semi-circle of diameter 14 cm along one of the rectangle's shorter sides. Using π = 22/7, find the perimeter of the compound shape.
   විසඳුම බලන්න

   Trace the outer boundary: the two long sides of the rectangle (20 cm each), the free short side (14 cm), and the semi-circular arc. The short side where the semi-circle is joined is internal and does not count. The semi-circle has radius r = 14/2 = 7 cm. Its arc length = πr = (22/7) × 7 = 22 cm. Perimeter = 20 + 20 + 14 + 22 = 76 cm.
   ආදර්ශයට ගත්තේ: modelled on the MATHEMATICS OL_10 exam pattern

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