Final answer:
To find the degree measure of the sector's arc, calculate the sector's angle in radians using the area formula and convert to degrees. Using the given area and radius, the angle is determined to be 144 degrees, which corresponds to option D.
Step-by-step explanation:
To find the degree measure of the arc of the sector in a circle with a radius of 10 cm and a sector area of 40 π square centimeters, we start by recalling that the area of a sector is given by the formula A = ½ r^2 θ, where r is the radius and θ is the angle in radians. To convert the angle to degrees, we use the fact that π radians equal 180 degrees. As the area A is given to be 40 π, we can set up the equation 40 π = ½ × 10^2 × θ to solve for θ in radians and then convert to degrees.
First, calculate θ in radians: 40 π = ½ × 100 × θ → θ = (40 π) / 50 = 0.8 π radians.
Next, convert θ to degrees: θ (in degrees) = 0.8 π × (180/π) = 144 degrees.
Therefore, the correct option is D) 144 degrees.