chords , my god!
Algebra
Level
3
A chord is the form of a square enclosing an area of 44 sq.cm.If the same chord is bent into a circle,then the area of the circle is?
Round off your answer.
52
50
44
cannot determine
56
40
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1 solution
I am not sure of the terminology, but I take it to mean there is a square with an area of 44
Therefore the side of the square is sqrt(44), and the perimeter is 4 x sqrt(44).
We need the circumference of the circle to equal the perimeter of the square.
2 x pi x r = 4 x sqrt(44)
Solving for r: note that sqrt(44) = 4 x sqrt(11)
r = ( 4 x 4 x sqrt(11))/ (2 x pi)
Area of circle = pi * r^2 = pi * (16 x sqrt 11)^2/(2 x pi)^2 = 16 x 11 / pi
Area = 56 sq. cm. rounded to nearest tenth.