The logo for a new company is a circle divided into 21 same-sized sectors. Three of the sectors are white, and the others are different colors.

The area of one of the white sectors is 13π/54 inches squared.

What is the radius of the circle? Enter your answer in the box rounded to the nearest hundredth.

 Apr 16, 2024

Here's how to find the radius of the circle:


Area of a Single White Sector:


We are given that the area of one white sector is 13π/54 square inches.


Proportion of White Sectors:


Since there are 21 sectors total and 3 are white, the white sectors represent 3/21 of the entire circle's area.


Full Circle Area:


To find the total area of the circle, we can divide the area of one white sector by its proportion (3/21) of the whole circle:


Total circle area = (Area of one white sector) / (Proportion of white sectors)


Total circle area = (13π/54 in²) / (3/21)


Circle Area Formula:


We know the area of a circle is calculated by πr², where r is the radius.


Equating Areas:


Since the total area we found represents the entire circle, we can equate it to the circle area formula:


πr² = (13π/54 in²) / (3/21)


Simplifying and Solving:


Cancel out common factors of π and simplify:


r² = (13 / 54) * (21 / 3) in²


r² = 13 in²


Take the square root of both sides (remembering that squaring can introduce extraneous solutions, so we'll check for those later).


r = √13 in ≈ 3.61 in (rounded to nearest hundredth)

 Apr 17, 2024

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