Find the area of sector when the radius is 5.6 and area at the centre is 135 given a pi of 22/7
Pls help me with my math (radius(5.6)(angle at center)
(135) find the area
not sure what "area at the centre" means
But I will say that if the arc of the sector subtends an angle θ, then its area is
a = 1/2 r^2 θ
To find the area of a sector, we need two pieces of information: the radius and the central angle.
Given:
Radius, r = 5.6
Central angle = 135 degrees
Value of pi, π = 22/7
Step 1: Convert the central angle to radians.
To convert degrees to radians, we use the conversion factor π radians = 180 degrees.
Central angle in radians = (135 degrees) × (π radians/180 degrees).
Central angle in radians = (135 degrees) × (22/7) radians/180 degrees).
Central angle in radians = 2.25 radians (rounded to two decimal places).
Step 2: Calculate the area of the sector.
The formula for the area of a sector is A = (θ/2) × r^2, where θ is the central angle and r is the radius.
Area of the sector = (2.25 radians/2) × (5.6)^2.
Area of the sector = (1.125) × (5.6)^2.
Area of the sector = (1.125) × (31.36).
Area of the sector ≈ 35.295 square units.
Therefore, the area of the sector with a radius of 5.6 and a central angle of 135 degrees is approximately 35.295 square units.
To find the area of a sector, you need to know the radius and the central angle. In this case, you have the radius (5.6) and the area at the center (135), but you don't have the central angle.
However, we can still find the central angle using the given information.
The area of a sector (A) is related to the central angle (θ) by the formula:
A = (θ/360) * π * r^2
First, substitute the given values into the formula:
135 = (θ/360) * (22/7) * (5.6^2)
To find θ, we can rearrange the formula:
θ = (360 * (135 / ((22/7) * 5.6^2)))
Now, plug in the values and calculate:
θ = (360 * (135 / ((22/7) * 5.6^2)))
≈ 181.64
Now that we have the central angle (θ ≈ 181.64), we can find the area of the sector using the formula:
A = (θ/360) * π * r^2
Plug the values into the formula:
A = (181.64/360) * (22/7) * (5.6^2)
≈ 50.31
Therefore, the area of the sector is approximately 50.31 square units.