In a diagram O is the centre of the circle,if angle<POQ is x and diameter is 7cm while the area of the shaded portion is 27.5cm^2.find correct to the nearest degree the value of x.(take pie as 22/7)
What diagram? Cannot copy and paste here.
To find the value of x, we need to first determine the area of the entire circle. The formula for the area of a circle is A = πr^2, where A is the area and r is the radius.
Since the diameter of the circle is given as 7 cm, the radius (r) is half of the diameter, which is 7/2 = 3.5 cm.
Substituting the value of r into the formula, we have:
A = π(3.5)^2
A = 22/7 * (3.5)^2
A ≈ 38.5 cm^2
Now, let's calculate the area of the shaded portion. We're given that the area is 27.5 cm^2.
The shaded portion is a sector of the circle, so the area of the sector can be calculated using the formula: Area of sector = (Angle/360°) * A
Substituting the given values, we have:
27.5 = (x/360°) * 38.5
To solve for x, we can rearrange the equation as:
x = (27.5 * 360°) / 38.5
Simplifying:
x ≈ 257.14°
Therefore, rounded to the nearest degree, the value of x is 257°.