A factory is printing a large square design on a circular tablecloth. The square design should be as large as possible. The tablecloth has an area of 30 square feet. What should be the maximum side length of the square design? What area of the tablecloth will not be printed with the square design?
Twilights Truth
Favorite Answer
Ok this is a multi step problem; first find the radius of the circle by working backwards from the area: 30=3.14*r^2, divide by 3.14 on both sides, 9.55=r^2, then take the square root of 9.55, r=3.09. So the radius is 3.09 and the diameter is 6.18. Now, if you draw a square on a circle, the diagonal between two opposite points is the diameter of the circle. Now to find the length of the sides we have to think of the square as two triangles and use the diameter in the Pythagorean theorem. Because it is a square, both sides are the same size so we can say 2*A^2=6.18^2, or 2*A^2=38.1924. Divide both sides by 2. A^2=19.0962. Find the square root A=4.37 each side of the square is 4.37 feet. Phew. Next step, area of the square is 4.37*4.37=19.1 feet ^2 Last step, 30 ft-19.1 feet= 10.9 feet^2 not taken up by the square. What a problem.
Anonymous
Draw a square on a smaller scale to the original keeping in mind how to get it back to the original and then take a compass, place the pin perfectly in the middle of the square, open it so that the lead is on the exact middle of a straight line of the square and draw a circle with out lifting or opening the compass any more. Take your formula to get the square back to its original size and apply it to your circle.