The marching band has ordered a banner with its logo. The logo is a circle with a 45 degree central angle. If the diameter of the circle is 3 feet, what is the length of the major arc to the nearest tenth?
8.2 ft
It’s right
circumf. = 3π feet
45° is 1/8 of a rotation.
so what is (1/8) of 3π ?
45
To find the length of the major arc, we need to first find the circumference of the circle using the formula:
Circumference = π * diameter
Given that the diameter is 3 feet, we can substitute this value into the formula:
Circumference = π * 3
Next, we need to find the length of the major arc. Since the central angle is 45 degrees, we can calculate the fraction of the circumference that the major arc represents.
To do this, we use the formula:
Arc Length = θ/360 * Circumference
Where θ is the central angle and the 360 is the total number of degrees in a circle.
Substituting the known values, we get:
Arc Length = (45/360) * (π * 3)
Simplifying, we have:
Arc Length = (1/8) * (3.14 * 3)
Arc Length ≈ 0.3927 * 3
Arc Length ≈ 1.1781 feet
Therefore, the length of the major arc, to the nearest tenth, is approximately 1.2 feet.