+14 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.
+1036 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)
