Answer:
Step-by-step explanation:
Given that,
The arc length is four times the radius
Let he radius be 'r'
Then, the arc length be 's'
The arc of a sector can be calculated using
s=θ/360 × 2πr
Then, given that s=4r
So, 4r = θ × 2πr / 360
Divide both side r
4 = θ × 2π/360
Then, make θ subject of formula
θ × 2π = 360 × 4
θ = 360 × 4 / 2π
θ = 720 / π
So, area of the sector can be determine using
A = θ / 360 × πr²
Since r = ¼s
Then,
A = (θ/360) × π × (¼s)²
A = (θ/360) × π × (s²/16)
A = θ × π × s² / 360 × 16
Since θ = 720 / π
A = (720/π) × π × s² / 360 × 16
A = 720 × π × s² / 360 × 16 × π
A = s² / 8
Then,
s² = 8A
Then,
s= √(8A)
s = 2 √2•A
120 seconds is 2 * 60s
60s is 1 minute, so 2*60s = 2 minutes
Answer:
616 cm^2
Step-by-step explanation:
Steps to derive the answer
1. we are going to first determine the radius from the circumference
2. we would calculate the area
Circumference of a circle = 2nr
n = 22/7
r = radius
88 = 2 x 22/7 x r
Divide both sides of the equation by 2 x 7/22
r = 14
Area of a circle = nr^2
3.14 x 14^2 = 616 cm^2
