SOLUTION: If a wire is bent into the shape of a square, then the area enclosed by the square is 81 cm square. when the same wire is bent into semi-circle. find the area enclosed by the semi-

Algebra ->  Circles -> SOLUTION: If a wire is bent into the shape of a square, then the area enclosed by the square is 81 cm square. when the same wire is bent into semi-circle. find the area enclosed by the semi-      Log On


   



Question 580602: If a wire is bent into the shape of a square, then the area enclosed by the square is 81 cm square. when the same wire is bent into semi-circle. find the area enclosed by the semi-circle
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+A+=+s%5E2+
+81+=+s%5E2+
+s+=+9+
The perimeter is +4s+
+P+=+4%2A9+
+P+=+36+ cm
This is the length of the wire
The circumference of a circle is
+C+=+2%2Api%2Ar+, or
+C+=+pi%2Ad+ where d is the diameter
A semi-circle enclosed by a wire looks like
+%281%2F2%29%2Api%2Ad+%2B+d+
+%281%2F2%29%2Api%2Ad+%2B+d+=+36+
+d%2A%28+pi%2F2+%2B+1+%29+=+36+
+d+=+36+%2F+%28+pi%2F2+%2B+1+%29+
The radius is
+r+=+18+%2F+%28+pi%2F2+%2B+1+%29+
The area of the semi-circle is
+A%2F2+=+%281%2F2%29%2Api%2Ar%5E2+
+A%2F2+=+%281%2F2%29%2Api%2A%28+18+%2F+%28+pi%2F2+%2B+1+%29%29%5E2+
+A%2F2+=+%281%2F2%29%2Api%2A%28+18+%2F+%28+1.5708+%2B+1+%29%29%5E2+
+A%2F2+=+%281%2F2%29%2Api%2A%28+18+%2F+2.5708+%29%5E2+
+A%2F2+=+%281%2F2%29%2Api%2A%28+7.0017+%29%5E2+
+A%2F2+=+%281%2F2%29%2Api%2A49.024+
+A%2F2+=+%281%2F2%29%2A154.013+
+A%2F2+=+77.0067+ cm
Hope I got it