A circle of radius 28cm is opened to form a square. What is the maximum possible area of the chord?
A chord does not have area. It is a line segment.
To find the maximum possible area of the chord, we need to consider the properties of a circle and a square.
First, let's understand the dimensions of the square formed by the circle. The diagonal of the square will be equal to the diameter of the circle. The diameter of the circle is twice the radius, so it is 2 * 28 cm = 56 cm.
Since the diagonal of the square is 56 cm, we can use the Pythagorean theorem to find the length of the sides of the square. Let's call the side length of the square "s". According to the Pythagorean theorem, the square of the diagonal is equal to the sum of the squares of the two sides.
Therefore, s^2 + s^2 = 56^2
2s^2 = 3136
s^2 = 3136 / 2
s^2 = 1568
s ≈ 39.60 cm (approximated to two decimal places)
Now, to find the maximum possible area of the chord, we need to consider the properties of a circle. The diameter of the circle is equal to the length of the diagonal of the square, which we found to be 56 cm.
The chord of a circle is the line segment that connects any two points on the circumference of the circle.
To determine the maximum area of the chord, we need to find the longest possible chord in the circle. This occurs when the chord is a diameter of the circle. Therefore, the maximum possible length of the chord in this case is equal to the diameter of the circle, which is 56 cm.
Finally, to find the maximum possible area of the chord, we can use the formula for the area of a circle with radius r:
Area of the circle = π * r^2
In this case, the radius of the circle is half of the diameter, so it is 56 cm / 2 = 28 cm.
Therefore, the maximum possible area of the chord is equal to the area of the circle with radius 28 cm:
Area of the chord = π * (28 cm)^2
Area of the chord ≈ 2463.08 cm^2 (approximated to two decimal places)