Final answer:
The claim that the area of the minor segment of a circle with a radius of 15 cm and a 60° angle at the center is 204478 cm² is false. The correct area calculation involves finding the sector's area and subtracting the area of the equilateral triangle within that sector.
Step-by-step explanation:
The statement regarding the area of the minor segment of the circle as 204478 cm² is false. To ascertain the correct area, we first find the area of the sector formed by the 60° angle. Since the angle is 1/6 of 360°, the sector's area would be 1/6 of the circle area. The area of the circle is πr², so the sector's area is (1/6) * π * 15² cm². We then subtract the area of the equilateral triangle with side length equal to the radius from the sector's area to find the area of the minor segment.
To calculate the area of the equilateral triangle formed with all sides equal to the radius of the circle (15 cm), we can use the formula √3/4 * a², where a is the length of a side. Subtracting the triangle's area from the sector's area gives us the area of the minor segment. Hence, the correct area would be significantly less than 204478 cm², indicating that the original claim is false.