If the circumference of a circle of radius r inches is equal to the perimeter of square with a side length of s inches, r/s=
A. 4/π
B. 2/π
C. √2/π
D. √2/π
E. 1/2π
I need help.
side of square = 2
so perimeter of square = 4s
circumference of circle with radius r is 2πr
so ...
2πr = 4s
πr = 2s
r/s = 2/π
To solve this problem, we need to understand the formulas for the circumference of a circle and the perimeter of a square.
1. The circumference of a circle can be calculated using the formula: C = 2πr, where C represents the circumference and r represents the radius of the circle.
2. The perimeter of a square can be calculated using the formula: P = 4s, where P represents the perimeter and s represents the side length of the square.
Now, let's work through the problem step by step:
Given: The circumference of a circle with radius r is equal to the perimeter of a square with side length s.
From what we know, we can equate the two expressions:
2πr = 4s
To solve for r/s, we need to isolate r and s on either side of the equation:
Divide both sides of the equation by 4:
(2πr) / 4 = s
Simplify:
πr / 2 = s
Now, we can solve for r/s:
r/s = (πr) / 2s
Since we want to express r/s in simplest form, we can cancel out common factors between numerator and denominator:
r/s = π/2
Therefore, the answer is B. 2/π.
I hope this explanation helps you understand how to approach and solve the problem.