The circle above has an area of 36 in2. What is the area of the yellow sector? Use 3.14 for .
42.39
Cannot see yellow sector. You cannot copy and paste here.
To find the area of the yellow sector, we first need to determine the angle of the sector.
Since the entire circle has an area of 36 in², the formula for the area of a circle is:
Area = π * r²
Given that the formula for the area of a sector is:
Area of Sector = (θ/360) * Area of Circle
We can rearrange the equation to solve for θ (the angle of the sector):
θ = (Area of Sector / Area of Circle) * 360
Now, substituting the given values:
Area of Circle = 36 in²
θ = (Area of Sector / 36) * 360
From the problem statement, we do not have the value of θ or the radius, so we cannot calculate the area of the yellow sector without additional information.
To find the area of the yellow sector, we need to first understand its relationship to the entire circle. A sector is a portion of a circle enclosed by two radii and an arc. The ratio of the angle formed by the sector to the total angle of a circle is equivalent to the ratio of the area of the sector to the total area of the circle.
In this case, we are given that the area of the entire circle is 36 in². Remember that the formula for the area of a circle is A = πr², where A is the area and r is the radius. Therefore, we can solve for the radius using the given area.
A = πr²
36 = 3.14 * r²
To find the radius (r), we rearrange the equation and solve for r:
r² = 36 / 3.14
r² ≈ 11.46
r ≈ √11.46
r ≈ 3.39 inches (rounded to two decimal places)
Now that we know the radius of the circle is approximately 3.39 inches, we can move on to finding the area of the yellow sector. To do this, we need to determine the angle formed by the yellow sector.
Since we don't have the specific angle measurement, let's assume it is θ. As mentioned earlier, the ratio of the angle of the sector to the total angle of the circle is equal to the ratio of the area of the sector to the total area of the circle. In this case, we know the total area of the circle (36 in²), so we can set up the following proportion:
θ / 360° = A_sector / A_circle
Since we are looking for the area of the sector, we rearrange the equation:
A_sector = (θ / 360°) * A_circle
Using the given value of π as 3.14, we substitute the known values into the equation:
A_sector = (θ / 360°) * 36 in²
A_sector = (θ / 360°) * 36
Now, we are left with solving for A_sector, the area of the yellow sector. However, we still need the angle measurement θ to find the exact value. Without the specific angle, we cannot calculate the area of the yellow sector.