A sector of a circle of a radius 6cm subrends angle of 105 at the centre of a circle.calculate the perimeter of the sector and the area of the sector?
Using area of a sector which is ∅/360 × π × r²
=105/360 × 22/7 × 6×6
=105/360 × 22/7 × 36
=105×22×36/360×7
=83160/2520=33cm2
An angle of 105 at the centre of a circle of radius 6 cm find the length of the arc and find the area of the sector
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A sector of a circle of radius 6cm subtends angle of 105 degrees at the centre of the circle. Calculate the perimeter and area of the sector
6+6+ 105/360*2*6*22/7
A sector of a circle 6cm has an angel of 1050 at the center. Calculate its
To calculate the perimeter and area of the sector, we need to use the formulas:
1. Perimeter of a sector = arc length + 2 * radius
2. Area of a sector = (angle/360) * π * radius^2
Given information:
- Radius of the circle = 6 cm
- Angle at the center = 105 degrees
Now let's calculate the perimeter and area of the sector step by step:
1. Perimeter of the sector:
Since the angle at the center is given as 105 degrees, we can find the arc length using the formula:
Arc length = (angle/360) * circumference of the circle
The circumference of the circle can be found using the formula:
Circumference = 2π * radius
Plugging in the values, we get:
Circumference = 2π * 6 cm
Next, calculate the arc length using the formula:
Arc length = (105/360) * (2π * 6 cm)
2. Radius of the sector:
The radius is already given as 6 cm.
3. Perimeter of the sector:
Perimeter = Arc length + 2 * Radius
Substituting the values, we get:
Perimeter = Arc length + 2 * 6 cm
Now, calculate the perimeter using the values obtained in step 1 and 3.
4. Area of the sector:
We can directly use the formula for the area of the sector:
Area = (angle/360) * π * radius^2
Substituting the given values, we get:
Area = (105/360) * π * (6 cm)^2
Now, calculate the area using the values obtained in step 4.
Perform the calculations using a calculator, and you will get the final values for the perimeter and area of the sector.
perimeter=2r+angle/360(2*22/7*r)
where r=6
angle =105
2*6+105/360=12.29
12.9(2*22/7*6)
12.29(37.71)
=463.4559
=463.46(2 d.p)
perimeter is the 2 radii, plus the outer arc
... 6 + 6 + [(105 / 360) * 2 * 6 * π]
area is the fraction of the circle
... (105 / 360) * π * 6^2