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WAEC 2009 · Paper 2 · Q11

  1. (a)

    A circle is inscribed in a square. If the sum of the perimeter of the square and the circumference of the circle is 100 cm, calculate the radius of the circle. [Take π=227\pi = \frac{22}{7}]

  2. (b)

    A rope 60 cm long is made to form a rectangle. If the length is 4 times its breadth, calculate, correct to one decimal place, the: (i) length; (ii) diagonal of the rectangle.

    Separate values with commas, e.g. 3, −2

Worked solution (try it first)

(a)

  1. The circle touches all four sides, so the side of the square is the diameter 2r2r.
  2. Perimeter of the square =4×2r=8r= 4 \times 2r = 8r.
  3. Circumference =2πr=447r= 2\pi r = \frac{44}{7}r.
  4. Add them: 8r+447r=1008r + \frac{44}{7}r = 100, so 1007r=100\frac{100}{7}r = 100.
  5. So r=7r = 7 cm.

(b)(i)

  1. Let the breadth be bb.
  2. The length is 4b4b.
  3. The rope is the perimeter: 2(4b+b)=602(4b + b) = 60.
  4. So 10b=6010b = 60 and b=6b = 6 cm.
  5. The length is 4×6=24.04 \times 6 = 24.0 cm.

(ii)

  1. Pythagoras: diagonal =242+62=612=24.7= \sqrt{24^2 + 6^2} = \sqrt{612} = 24.7 cm.

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