saiesta wrote:
An artist is painting a white circular region on the top surface of a square blue tile that measures 8 inches on a side. If the circle is inscribed in the square, what fraction of the top surface of the tile will be blue?
A. \(\frac{1}{4}\)
B. \(\frac{1}{2}\)
C. \(\frac{\pi}{4}\)
D. \(\frac{(4 – \pi)}{\pi}\)
E. \(\frac{(4 – \pi)}{4}\)
Attachment:
Untitled.png
Area of Square is \(8^2\) = 64
Area of circle is \(π*4^2\) = \(16π\)
Area of Blue region is \(64 - 16π\)
So, Fraction of tile that will be Blue is = \(\frac{64 - 16π}{64}\)
Or, Fraction of tile that will be Blue is = \(\frac{16 (4 - π)}{16*4}\) = \(\frac{4 - π}{4}\)
Hence, Correct answer will be (E) \(\frac{4 - π}{4}\)Thank you very much for the explanation. I misread the question. I thought that we were being asked for the blue area, but I see now that we HAVE to divide by 64 as we are being asked for the fraction of the blue area to the square.