Answer:
a. 1.95 cm.
b. 3920 cm^2.
Explanation:
(a) To find the length of the arc that subtends the central angle theta on a circle of diameter d, we can use the formula:
Arc Length = (theta / 360°) x (pi x d)
Substituting the given values, we get:
Arc Length = (1.6 / 360°) x (pi x 140 cm)
Arc Length ≈ 1.95 cm
Therefore, the length of the arc that subtends the central angle of 1.6 radians on a circle of diameter 140 cm is approximately 1.95 cm.
(b) To find the area of the sector determined by the central angle theta, we can use the formula:
Area of Sector = (theta / 2π) x pi x (r^2)
where r is the radius of the circle.
Since the diameter of the circle is given as 140 cm, the radius is half of that, which is 70 cm.
Substituting the given values, we get:
Area of Sector = (1.6 / (2 x pi)) x pi x (70 cm)^2
Area of Sector ≈ 3920 cm^2
Therefore, the area of the sector determined by the central angle of 1.6 radians on a circle of diameter 140 cm is approximately 3920 cm^2.