Final answer:
The angle subtended by the arc that is 1/5 of the circle's circumference is 72 degrees, which is found by taking 1/5 of 360 degrees due to the proportionality of arc length and central angle.
Step-by-step explanation:
Finding the Angle Subtended by an Arc
To find the angle subtended by an arc at the center of the circle, we can use the relationship between the arc length, the radius of the circle, and the central angle. As you mentioned, for a full revolution, the arc length (which we can denote as As) would be the circumference of the circle, which is 2πr (where r is the radius and π is Pi, approximately 3.14159). The corresponding angle for a full revolution is 360 degrees or 2π radians, establishing a proportional relationship between the arc length and the angle.
Given that the arc in question is 1/5 of the circle's circumference, the angle subtended, in radians, is also 1/5 of 2π, which is 2π/5 radians. To express this angle in degrees, you would multiply by (180/π) to get 72 degrees.
Furthermore, knowing the area of the circle is 346.5 cm², we could also find the radius using the formula A = πr², but in this case, the radius is not required to calculate the subtended angle since we already have the proportion of the arc length to the circumference.