What is the area of the sector, in square units, determined by an arc with a measure 45° in a circle with radius 6? Round to the nearest tenth.
A sector with an arc subtended by a 45° angle is 1/8 of the circle
Area of the whole circle = π(6)^2 = 36π
can you finish it?
To find the area of the sector, we need the formula:
Area = (θ/360°) * π * r^2
Given:
θ = 45°
r = 6
Plugging in the values:
Area = (45°/360°) * π * 6^2
Area = (0.125) * π * 6^2
Area = (0.125) * π * 36
Area ≈ 4.5π
Rounding to the nearest tenth:
Area ≈ 4.5 * 3.14
Area ≈ 14.1 square units
Therefore, the area of the sector, rounded to the nearest tenth, is approximately 14.1 square units.
To find the area of the sector, we can use the formula A = (θ/360) * π * r^2, where A is the area, θ is the angle of the sector, π is a mathematical constant approximately equal to 3.14159, and r is the radius of the circle.
In this case, the angle of the sector is 45° and the radius is 6 units.
First, we substitute these values into the formula:
A = (45/360) * π * (6^2)
Next, we simplify the calculation:
A = (1/8) * 3.14159 * 36
A = 0.125 * 3.14159 * 36
A = 4.71238
Rounding to the nearest tenth, the area of the sector is approximately 4.7 square units.