To find length of arc of a sector, we will use the formula
s = rθ
Length of arc is part of the circumference of the circle, the picture clearly shows.
Here s is the length of arc.
Problem 1 :
s = 12π/5 ; θ = π/2 ; r = ?
Solution :
Arc length of the circle s = rθ
12π/5 = r × π/2
12π/5 × 2/π = r
24/5 = r
So, the radius r is 24/5 .
Problem 2 :
s = 50π/3 in ; θ = 5π/6 ; r = ?
Solution :
Arc length of the circle s = rθ
50π/3 = r × 5π/6
50π/3 × 6/5π = r
20 = r
So, the radius r is 20 .
Problem 3 :
s = 7ft ; θ = 3π/4 ; r = ?
Solution :
Arc length of the circle s = rθ
7 = r × 3π/4
7 × 4/3π = r
28/3π = r
28/(3 × 22/7) = r
196/66 = r
So, the radius r is 196/66 ft .
Problem 4 :
s = 20 cm ; θ = 2π/3 ; r = ?
Solution :
Arc length of the circle s = rθ
20 = r × 2π/3
20 × 3/2π = r
60/2π = r
30/(22/7) = r
So, the radius r is 105/22 cm .
Problem 5 :
s = 12 in ; θ = 5 ; r = ?
Solution :
Arc length of the circle s = rθ
12 = r ×5
12/5 = r
So, the radius r is 12/5 in.
Problem 6 :
s = 7 in ; θ = 3 ; r = ?
Solution :
Arc length of the circle s = rθ
7 = r × 3
7/3 = r
So, the radius r is 7/3 in.
Problem 7 :
s = 15 m ; θ = 270 ; r = ?
Solution :
Arc length of the circle s = rθ
15 = r × 270
15/270 = r
1/18 = r
So, the radius r is 1/18 m.
Problem 8 :
s = 8 yd ; θ = 225 ; r = ?
Solution :
Arc length of the circle s = rθ
8 = r × 225
8/225 = r
28.125 = r
So, the radius r is 28.125 yd.
May 21, 24 08:51 PM
May 21, 24 08:51 AM
May 20, 24 10:45 PM