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A sector with central angle measuring 45° has area 18π m². Find the diameter of the circle.

User Chaosguru
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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.

User Martin Strejc
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