If a radius of circle 9cm angle at center 105°what are length of arc and perimeter of actor
I assume you mean perimeter of sector (not actor!)
105° = 7π/12
arc length s = rθ = 9 * 7π/12 = 21π/4
perimeter p = 2r+s = 18 + 21π/4
Why did the circle go on a diet? Because it wanted to have a lean circumference!
To find the length of the arc, we need to use the formula:
Arc length = (angle / 360°) x (2πr)
Given that the radius is 9cm and the angle at the center is 105°, substituting the values into the formula, we get:
Arc length = (105° / 360°) x (2π(9cm))
Now, let's do some math magic:
Arc length = (7/24) x (18π)
Arc length = (7/4) x (3π)
Arc length = 21π/4 cm
So, the length of the arc is 21π/4 cm.
As for the perimeter of the actor... oops, I meant the perimeter of the sector, we need to calculate the sum of the length of the arc and the two radii.
Perimeter of the sector = Arc length + 2r
Substituting the given values, we get:
Perimeter of the sector = 21π/4 + 2(9cm)
Perimeter of the sector = 21π/4 + 18cm
Well, there you have it. The length of the arc is 21π/4 cm, and the perimeter of the sector is 21π/4 + 18cm. Just remember, when it comes to geometry, humor is always in the right angle!
To find the length of the arc, we can use the formula:
Length of Arc = (θ/360) * (2π * r),
where θ is the angle at the center of the circle and r is the radius.
Given that the radius is 9 cm and the angle at the center is 105°, we can substitute these values into the formula to calculate the length of the arc:
Length of Arc = (105/360) * (2π * 9)
= (7/24) * (2π * 9)
= (7/24) * (18π)
= (7/4) * π
= 7π/4
≈ 5.497 cm.
To find the perimeter of the sector, we need to add the length of the arc to the sum of the radii:
Perimeter of Sector = Length of Arc + 2 * r
= 5.497 + 2 * 9
= 5.497 + 18
= 23.497 cm.
Therefore, the length of the arc is approximately 5.497 cm and the perimeter of the sector is approximately 23.497 cm.
To find the length of an arc, you can use the formula:
Length of Arc = (Angle ÷ 360) x 2πr
where Angle is the measure of the angle formed by the arc at the center of the circle, and r is the radius of the circle.
In this case, the radius of the circle is given as 9 cm, and the angle at the center is 105°.
Length of Arc = (105° ÷ 360) x (2 x 3.14 x 9)
Length of Arc = (0.2917) x (56.52)
Length of Arc ≈ 16.44 cm
So, the length of the arc is approximately 16.44 cm.
To find the perimeter of the sector, you need to add the length of the arc to the sum of the radii of the sector (twice the radius of the circle).
Perimeter of Sector = Length of Arc + 2r
Perimeter of Sector = 16.44 + (2 x 9)
Perimeter of Sector = 16.44 + 18
Perimeter of Sector ≈ 34.44 cm
So, the perimeter of the sector is approximately 34.44 cm.