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 15.96 centimeters longer than the perimeter of the square, find the length of a radius of the circle. (Use 3.14 as an approximation for π .)
A) 9.28 centimeters
B) 7 centimeters
C) 6.75 centimeters
D) 7.25 centimeters
E) 2.28 centimeters

Question

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 15.96 centimeters longer than the perimeter of the square, find the length of a radius of the circle. (Use 3.14 as an approximation for π .)
A) 9.28 centimeters
B) 7 centimeters
C) 6.75 centimeters
D) 7.25 centimeters
E) 2.28 centimeters

Quizplus · Accepted Answer

The length of the radius (r) is equal to the side of the square (s). The circumference of the circle is $2\pi r$ and the perimeter of the square is $4s$. Given that the circumference of the circle is 15.96 cm longer than the perimeter of the square, we have $2\pi r = 4s + 15.96$. Since $r = s$, we can substitute $s$ with $r$ to get $2\pi r = 4r + 15.96$. Using $3.14$ for $\pi$, we get $2(3.14)r = 4r + 15.96$, which simplifies to $6.28r = 4r + 15.96$. Solving for $r$, we subtract $4r$ from both sides to get $2.28r = 15.96$, and dividing both sides by $2.28$ gives $r = 7$ centimeters.

Suppose That the Length of a Radius of a Circle