Theory question 104
Number Bases(a) Divide 11111111two by 101two
(b) A sector of a circle 6cm has an angle of 105° at the centre. Calculate its (i) perimeter (ii) area (Take π = 22/7)
Show the model answer
Model answer
(a) 11111111two = 255 and 101two = 5; 255 ÷ 5 = 51 = 110011two (or by long division in base two)
(b)(i) Arc = 105/360 × 2 × 22/7 × 6 = 11 cm; perimeter = 11 + 6 + 6 = 23 cm
(ii) Area = 105/360 × 22/7 × 62 = 33 cm2
Explanation
The perimeter of a sector includes the two radii as well as the arc.