the area of a circle of diameter 126cm is 4158cm^2 calculate the substended at the centre of a circle
a = 1/2 r^2 θ
So plug in your numbers to find θ
And it always helps to write the question correctly. I think you meant
the area of a sector of a circle of diameter 126cm is 4158cm^2. Calculate the angle subtended at the centre of the circle.
Help meh with that question
To find the angle subtended at the center of a circle, you need to know the radius (r) and the length of the arc (s).
1. Calculate the radius (r) using the diameter (d):
r = d / 2
r = 126 cm / 2
r = 63 cm
2. Calculate the circumference (C) of the circle using the radius:
C = 2 * π * r
C = 2 * 3.14 * 63 cm
C ≈ 395.64 cm
3. Calculate the angle (θ) subtended at the center of the circle using the length of the arc (s) and the circumference (C):
θ = (s / C) * 360°
θ = (4158 cm^2 / 395.64 cm) * 360°
θ ≈ 3779.785°
Therefore, the angle subtended at the center of the circle is approximately 3779.785°.
To calculate the subtended angle at the center of a circle, we need to use the formula:
Subtended angle = (Arc length / Radius) * (180° / π)
In this case, we are given the area of the circle and the diameter, but we need to find the radius. We know that the formula for the area of a circle is:
Area = π * (Radius^2)
First, let's find the radius using the given diameter:
Diameter = 126 cm
Radius = Diameter / 2 = 126 cm / 2 = 63 cm
Now we can substitute the given values into the formula for the area to find the value of π:
4158 cm^2 = π * (63 cm)^2
To solve for π, divide both sides of the equation by (63 cm)^2:
4158 cm^2 / (63 cm)^2 = π
Now we can calculate the value of π:
π ≈ 4158 cm^2 / (63 cm)^2 ≈ 3.14
Next, we can calculate the subtended angle using the formula:
Subtended angle = (Arc length / Radius) * (180° / π)
Since we are not given the length of the arc, we cannot calculate the subtended angle without this information. The subtended angle depends on the length of the arc, which is not specified in the given information.
Therefore, we cannot calculate the subtended angle without further information.