Question

A wire bent into the shape of a square encloses an area of 25 cm squared. Then the same wire is cut and bent into two identical circles. What is the radius of one of the circles?

Answer 1

Area of both circles combined = 25
\[2πr^2 = 25\]
\[r^2 = \frac{25}{2π}\]
\[r = \sqrt{\frac{25}{2π}}\]

Answer 2

since area of square = 25cm^2 => its side = sqroot(25cm^2) = 5 cm
then length of wire = perimeter of square = 4 * 5cm = 20 cm

Answer 3

for two identical circles, the sum of their circumferences has to be equal to the length of the wire ie. 20 cm (since same wire is to be used)
circumference of a circle = 2πr and for two circles = 2* 2πr = 4πr
so 4πr = 20 cm
r = 20/4π cm = 5/π cm
r = 1.6 cm


This is the right solution because the length of the wire remains same. The question does not say sum of the areas of the circle equals area of the square because for the same boundary length the area of the square is NEVER EQUAL to the are of the circle!!!!!

so r = 5/π cm or 1.6 cm