Answer:
about 12.67 cm²
Explanation:
The area of a sector of a circle is given by:
A = (θ/360) x πr²
where A is the area of the sector, θ is the central angle of the sector (in degrees), and r is the radius of the circle.
In this case, we are given the central angle of the sector, which is 86.4 degrees, and the radius of the circle, which is 4.1 cm. Therefore, we can calculate the area of the sector formed by angle CBA as follows:
A = (86.4/360) x π(4.1)²
A ≈ 12.67 cm²
So, the area "about 12.67 cm²" is a possible area of the sector formed by angle CBA.
To determine if any of the other given areas are possible, we can calculate the central angle of each sector using the same formula as above, and then check if it matches the given angle of 86.4 degrees.
For the area "about 23.35 cm²":
23.35 = (θ/360) x π(4.1)²
θ ≈ 149.6 degrees
The central angle of this sector is approximately 149.6 degrees, which is not equal to the given angle of 86.4 degrees. Therefore, the area "about 23.35 cm²" is not a possible area of the sector formed by angle CBA.
For the area "about 3.09 cm²":
3.09 = (θ/360) x π(4.1)²
θ ≈ 19.16 degrees
The central angle of this sector is approximately 19.16 degrees, which is not equal to the given angle of 86.4 degrees. Therefore, the area "about 3.09 cm²" is not a possible area of the sector formed by angle CBA.
For the area "about 40.14 cm²":
40.14 = (θ/360) x π(4.1)²
θ ≈ 256.4 degrees
The central angle of this sector is approximately 256.4 degrees, which is not equal to the given angle of 86.4 degrees. Therefore, the area "about 40.14 cm²" is not a possible area of the sector formed by angle CBA.
Therefore, the only possible area of the sector formed by angle CBA is "about 12.67 cm²".