Suppose that the length of a radius of a circle is the same as the length of a side of a square. If the circumference of the circle is 6.84 centimeters longer than the perimeter of the square, find the length of a radius of the circle. (Use 3.14 as an approximation for $\pi$ .)
A) 2.28 centimeters
B) 5.28 centimeters
C) 3 centimeters

Question

Quizplus · Accepted Answer

Given that the length of a radius (r) of the circle is the same as the length of a side (s) of the square, we have $r = s$. The circumference of the circle is given by $C = 2\pi r$, and the perimeter of the square is $P = 4s$. According to the problem, the circumference of the circle is 6.84 centimeters longer than the perimeter of the square, so we have $2\pi r = 4s + 6.84$. Since $r = s$, we can substitute $s$ with $r$ in the equation: $2\pi r = 4r + 6.84$. Using $\pi = 3.14$, we get $2(3.14)r = 4r + 6.84$. Simplifying, we find $6.28r = 4r + 6.84$, and solving for $r$, we get $r = 3$ centimeters.

Suppose That the Length of a Radius of a Circle π\piπ

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