Final answer:
To find the diameter of the circle from a sector with a 45° central angle and an area of 18π m², set up a proportion between the sector area and the circle area, solve for the radius, and then double it to find the diameter, which is 24 meters.
Step-by-step explanation:
The question asks to find the diameter of the circle given that a sector with a central angle measuring 45° has an area of 18π m². The area of the sector is a fraction of the area of the circle, proportional to the angle of the sector out of 360°.
Step 1: Establish the proportion between the sector area and the whole circle area.
Area of sector / Area of circle = Central angle / 360
18π / (πr²) = 45 / 360
Step 2: Solve for r².
1/8 = 18π / (πr²)
r² = 144
Step 3: Find the radius, r.
r = √144
r = 12 m
Step 4: Calculate the diameter, D.
D = 2r
D = 2(12 m)
D = 24 m
Therefore, the diameter of the circle is 24 meters.