The radius of a circular field and the side length of a square field are…
2023
The radius of a circular field and the side length of a square field are equal. Find the ratio of their perimeters. (Take π = 22/7.)
Answer: D. 11 : 7 — CONCEPTFor a circle with radius r, the perimeter is 2πr. For a square with side s, the perimeter is 4s. When r and s are equal, the common length cancels from…
- A.
2 : 1
- B.
1 : 2
- C.
4 : 7
- D.
11 : 7
Show answer & explanation
Correct answer: D
CONCEPT
For a circle with radius r, the perimeter is 2πr. For a square with side s, the perimeter is 4s.
When r and s are equal, the common length cancels from their perimeter ratio, so only the numerical coefficients need to be compared.
APPLICATION
Let the common radius and side length be x.
The required ratio is 2πx : 4x. Cancelling 2x gives π : 2.
Using π = 22/7, the ratio becomes 22/7 : 2 = 22 : 14 = 11 : 7.
CROSS-CHECK
Taking x = 7 units gives perimeters 44 units and 28 units; 44 : 28 simplifies to 11 : 7, confirming the calculation.
Therefore, the ratio of the circular field's perimeter to the square field's perimeter is 11 : 7.