Areas Related to Circles · Class 10 · CBSE Mathematics

If the perimeter of a semi-circular protractor is 36 cm, find its diameter. (Use pi = frac{22}{7})

Practice question from Areas Related to Circles (Class 10 · CBSE Mathematics), with the correct answer and a step-by-step solution.

medium · MCQ · Q-1C9C6C

If the perimeter of a semi-circular protractor is 36 cm, find its diameter. (Use π=227\pi = \frac{22}{7})

  1. A.7 cm
  2. B.14 cmCorrect answer
  3. C.21 cm
  4. D.28 cm

Solution

The perimeter of a semi-circle is given by πr+2r=r(π+2)\pi r + 2r = r(\pi + 2). Given perimeter is 36 cm. So, r(227+2)=36  ⟹  r(367)=36  ⟹  r=7r(\frac{22}{7} + 2) = 36 \implies r(\frac{36}{7}) = 36 \implies r = 7 cm. The diameter is 2r=2×7=142r = 2 \times 7 = 14 cm.

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