Theory question 109
Commercial Arithmetic(a) Mrs Otoo spends 1/9 of her monthly salary on rent, 1/2 on food, 1/4 on clothes and still had $195.00 left. How much does she earn in a month? (b) A sector of a circle of radius 6 cm subtends an angle of 105° at the centre. Calculate the: (i) perimeter; (ii) area, of the sector [Take π = 22/7]
Show the model answer
Model answer
(a) Spent 1/9 + 1/2 + 1/4 = 31/36, so 5/36 of salary = $195 ⇒ salary = 195 × 36 ÷ 5 = $1,404
(b)(i) Arc = 105/360 × 2 × 22/7 × 6 = 11 cm; perimeter = 6 + 6 + 11 = 23 cm
(ii) Area = 105/360 × 22/7 × 6² = 33 cm²
Explanation
The perimeter of a sector includes the two radii.