A sector of a circle subtends an angle of 105° at the centre of the circle calculate the perimeter and area of the circle
Missing data.
If the radius is r
the perimeter of a circle is 2πr
the area of a circle is π r^2
Your sector is 105/360 or 7/24 of the area
and the arc length of your sector is 7/24 of the perimeter
I are mad👹
To calculate the perimeter and area of the circle, we need to know either the radius or diameter of the circle. Do you have that information?
To calculate the perimeter and area of the circle, we need to know either the radius or the diameter of the circle.
Let's assume we know the radius of the circle (r).
To find the perimeter of the circle, we use the formula:
Perimeter = 2 * π * r
Here, π (pi) is a mathematical constant approximately equal to 3.14159.
To find the area of the circle, we use the formula:
Area = π * r^2
Now, to solve the problem, we need to calculate the radius. Since we know that the sector subtends an angle of 105° at the center of the circle, we can use that information:
The angle of the sector is 105°, and the full angle of a circle is 360°. Thus, the ratio of the angle of the sector to the full angle of the circle is:
105° / 360° = 7/24
Since the sector is a fraction of the entire circle, we can deduce that the sector area (A_sector) is also a fraction of the entire circle's area (A_circle). Therefore, the ratio of the sector area to the circle's area is also 7/24.
We also know that the sector area formula is given by:
A_sector = (θ/360°) * π * r^2
Where θ is the angle of the sector.
Substituting the given values, we get:
7/24 = (105° / 360°) * π * r^2
Now, let's solve this equation to find the radius (r):
(105/360) * π * r^2 = (7/24)
Now solve for r:
r^2 = (7/24) * (360° / 105°) * 1/π
r^2 = (7/24) * (4/3) * (1/π)
r^2 = (28/72) * (1/π)
r^2 = (7/18) * (1/π)
r = sqrt((7/18) * (1/π))
After calculating the value of r, plug it into the formulas for perimeter and area to find the respective values.
Perimeter = 2 * π * r
Area = π * r^2