To find the angle of the sector, we can use the formula:
Area of sector = (θ/360)πr^2
Given that the area of the sector is 55 cm^2 and the radius is 10 cm, we can plug in the values:
55 = (θ/360) * (22/7) * 10^2
55 = (θ/360) * 220
55 = 22θ/7
θ = (55 * 7)/22
θ = 35 degrees
So, the angle of the sector is 35 degrees.
To find the area of the shaded segment, we need to subtract the area of the sector from the area of the sector minus the area of the triangle formed by the sector.
Area of segment = Area of sector - Area of triangle
Area of sector = (35/360) * (22/7) * 10^2
= (7/18) * 220
= 85/2 cm^2
The triangle is an isosceles triangle with two equal sides as the radius of the circle (10 cm) and the base angle of 35 degrees. We can calculate the height using the formula:
height = (10) * sin(35)
≈ 5.74 cm
Area of triangle = (1/2) * base * height
= (1/2) * 10 * 5.74
≈ 28.7 cm^2
Therefore, Area of segment = 85/2 - 28.7
= 85/2 - 57.4
= 27/2 cm^2
Hence, the area of the shaded segment is 27/2 cm^2.
A sector of a circle has an area of 55cm^2. If the radius of the circle is 10cm. Calculate the angle of the sector. (Use π=22/7)
Calculate the area of the shaded segment in a circle (leave your answer in the terms of π)
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1 answer