If the perimeter of a circle equals the perimeter of a square, the ratio of…
2023
If the perimeter of a circle equals the perimeter of a square, the ratio of their areas (circle : square) is:
Answer: C. 14 : 11 — ConceptFor equal perimeters, express both areas in terms of one dimension before forming their ratio. A circle has perimeter 2πr and area πr2; a square has…
- A.
4 : 1
- B.
11 : 7
- C.
14 : 11
- D.
More than one of the above
- E.
None of the above
Attempted by 9 students.
Show answer & explanation
Correct answer: C
Concept
For equal perimeters, express both areas in terms of one dimension before forming their ratio.
A circle has perimeter 2πr and area πr2; a square has perimeter 4s and area s2.
Application
Set the perimeters equal: 2πr = 4s.
Solve for the square’s side: s = πr/2.
Square the side to obtain the square’s area: s2 = π2r2/4.
Form the area ratio: πr2 : π2r2/4 = 4 : π.
Use the convention applied by the official BPSC key, π = 22/7: 4 : 22/7 = 28 : 22 = 14 : 11.
Cross-check
Numerically, 4/π ≈ 1.2732 and 14/11 ≈ 1.2727. The small difference is due to replacing π by 22/7.
Therefore, under the exam convention confirmed by the official BPSC answer key, the answer is 14 : 11.