Question 58813
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 greater than the perimeter of the square, find the length of a radius of the circle. (Use 3.14 as an approximation for Pi.
:
Let x = length of the side & the radius
:
Perimeter of the square: 4x
:
Circumference of the circle: 2*pi*x
:
"circumference of the circle is 15.96 cm greater than the perimeter of the sq."
(2*pi*x) = 4x + 15.96
6.28x = 4x + 15.96
6.28x - 4x = 15.96
2.28x = 15.96
x = 15.96/2.28
x = 7 cm
:
Check our solution x = 7:
Circum - perimeter   
(2*pi*7) - 4(7) =
43.96 - 28 = 15.96