In a circle of radius 12 inches, a sector is formed by a central angle of pie/4 radians. Find the area of the sector to the nearest hundredth of a square inch.
Area of whole circle = π(12^2) = 144π
π/4 radians = 45° or 1/8 of a circle
so the area of your sector = 144π/8 =56.55
To find the area of a sector, you can use the formula:
Area = (θ/2) × r²
where θ represents the central angle and r represents the radius of the circle.
Given that the radius of the circle is 12 inches and the central angle is π/4 radians, we can substitute these values into the formula:
Area = (π/4)/2 × 12²
Simplifying this expression:
Area = (π/8) × 144
Area = (π/8) × 144
Now, let's calculate the area:
Area ≈ 3.14/8 × 144
Area ≈ 0.3927 × 144
Area ≈ 56.55
Therefore, the area of the sector is approximately 56.55 square inches when rounded to the nearest hundredth.
To find the area of a sector, you can use the formula:
Area of sector = (central angle / 2π) × πr^2
Given that the central angle of the sector is π/4 radians and the radius of the circle is 12 inches, we can substitute these values into the formula:
Area of sector = (π/4 / 2π) × π(12^2)
First, let's simplify the fraction (π/4 / 2π) by canceling out the π terms:
Area of sector = (1/4 / 2) × π(12^2)
Simplifying further:
Area of sector = (1/8) × π(144)
Next, calculate the product of 1/8 and 144:
Area of sector = (18) × π
To find the area of the sector to the nearest hundredth of a square inch, we need to calculate the value of π and round the result:
Area of sector ≈ 56.55 square inches
Therefore, the area of the sector to the nearest hundredth of a square inch is approximately 56.55 square inches.