Answer:628.319 cm^2
Explanation:
The area of a sector of a circle can be found by using the formula:
Area = (angle/360) * pi * r^2
where angle is the measure of the central angle of the sector in degrees, pi is a mathematical constant approximately equal to 3.14159, and r is the radius of the circle.
In this case, the radius of the circle is given as 40 cm and the central angle is 45 degrees.
To find the area, we can substitute these values into the formula:
Area = (45/360) * 3.14159 * 40^2
Simplifying this equation:
Area = (0.125) * 3.14159 * 1600
Area ≈ 628.319 cm^2
So, the area of the sector of a circle with a radius of 40 cm and a central angle of 45 degrees is approximately 628.319 cm^2.