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)
well, to find x recall the area of a sector, so you want
(1/2)(3.5^2)x = 27.5
x is in radians, so you will have to convert to degrees.
To solve this problem, we need to find the value of x, which represents the angle <POQ.
First, let's draw a diagram to visualize the given information. You have a circle, with O as the center, and <POQ as an angle within the circle. The diagram may also show a shaded region within the circle.
Since the diameter is given as 7 cm, we can find the radius by dividing the diameter by 2. Thus, the radius (r) is 7/2 = 3.5 cm.
To find the area of the shaded portion, we need to know the formula for the area of a sector. A sector is a portion of a circle enclosed by two radii and the corresponding arc. The formula for the area of a sector is:
Area of Sector = (x/360) * π * r^2
In our case, we know the area of the shaded portion is 27.5 cm^2. So, we can set up the following equation:
27.5 = (x/360) * (22/7) * (3.5)^2
To solve for x, we need to isolate it on one side of the equation. Let's go through the steps:
1. Multiply both sides of the equation by 360 to eliminate the fraction:
27.5 * 360 = x * (22/7) * (3.5)^2
2. Simplify:
9900 = x * (22/7) * 12.25
3. Divide both sides of the equation by 12.25 * (22/7) to solve for x:
x = (9900 / (12.25 * 22/7))
Evaluate the right side of the equation separately:
x = (9900 / (12.25 * 22/7))
x = (9900 / 85.25)
x ≈ 116.21
Therefore, to the nearest degree, the value of x is approximately 116 degrees.