Theory question 110
Mensuration of Plane Shapes(a) A segment of a circle is cut off from a rectangular board as shown in the diagram. If the radius of the circle is 1½ times the length of the chord, calculate, correct to 2 decimal places, the perimeter of the remaining portion. [Take π = 22/7]
(b) Evaluate without using calculators or tables, (3/√3)(2/√3 − √12/3).
Show the model answer
Model answer
(a) Chord = 22 − 5 − 3 = 14 cm, so the radius = 21 cm.
sin(½θ) = 7/21 → ½θ ≈ 19.47° → θ ≈ 38.94°.
Arc = 38.94/360 × 2 × 22/7 × 21 ≈ 14.28 cm.
Perimeter = 22 + 12 + 12 + 5 + 3 + 14.28 = 68.28 cm.
(b) 3/√3 = √3 and √12/3 = 2√3/3. √3 × 2/√3 − √3 × 2√3/3 = 2 − 2 = 0.
Explanation
The curved edge replaces the 14 cm chord in the perimeter.