UPSC Prelims 1998·GS1·science-and-technology·science and technology

LMNOP, is a semi-circle with centre at R and diameter LP, LSR and RQP are also semi-circles with centres at T and U and diameters LR = RP = 1/2 LP. The ratio of perimeters of LMNOP and LSRQP is

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Last updated 23 May 2026, 3:31 pm IST
  1. A0.75: 1
  2. B1: 1Correct
  3. C1: 0.75
  4. D1.25: 1

Explanation

To solve this, let the radius of the large semi circle LMNOP be r. The diameter LP is therefore 2r. The perimeter of a semi circle is the length of its curved arc. 1. For the large semi circle LMNOP: The length of the curved arc is pi times r. 2. For the smaller shape LSRQP: This path consists of two smaller semi circles, LSR and RQP. The diameter of each small semi circle is r, so the radius of each is r/2. 3. Calculating LSRQP: The curved arc of LSR is pi times r/2. The curved arc of RQP is also pi times r/2. Adding them together gives pi times r/2 plus pi times r/2, which equals pi times r. Comparing the two results, the perimeter of LMNOP is pi times r and the perimeter of LSRQP is also pi times r. Therefore, the ratio is 1 to 1. Correct option is B.
science-and-technology: LMNOP, is a semi-circle with centre at R and diameter LP, LSR and RQP are also semi-circles with centres at T and U and
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