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The logo for a new company is a circle divided into 16 same-sized sectors. Four of the sectors are white, and the others are different colors. The area of one of the white sectors is 3π/28 inches squared. What is the radius of the circle? Enter your answer in the box rounded to the nearest hundredth.

User Luart
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1 Answer

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To find the radius of the circle, we need to determine the area of one sector and then use it to calculate the radius.

Given that the area of one of the white sectors is 3π/28 square inches, we can set up the equation:

Area of one white sector = (3π/28) square inches

The area of a sector can be calculated using the formula:

Area of a sector = (θ/360) * π * r^2

Where θ is the central angle of the sector and r is the radius of the circle.

Since there are 16 sectors, the central angle of each sector is 360°/16 = 22.5°.

Now we can set up the equation:

(22.5/360) * π * r^2 = (3π/28)

Simplifying the equation:

(22.5/360) * r^2 = (3/28)

Dividing both sides of the equation by (22.5/360):

r^2 = (3/28) * (360/22.5)

r^2 = 15.75

Taking the square root of both sides:

r = √(15.75)

Calculating the approximate value of the radius to the nearest hundredth:

r ≈ 3.97

Therefore, the radius of the circle is approximately 3.97 inches.

User Gawi
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