Final answer:
To calculate the radius of a circle given the arc length and angle, the angle is first converted to radians, and then the arc length formula is applied to find the radius. Using the given arc length of 88 cm and angle of 144 degrees, the radius is determined to be 35 cm.
Step-by-step explanation:
To find the radius of a circle if the arc length is 88 cm and the arc subtends an angle of 144° at the centre, we can use the formula for arc length that relates the arc length to the angle and the radius. Since we are given that π = 22/7 for calculation purposes, we can express the angle in radians to use it in the formula.
The circumference of a circle is given by C = 2πr, where r is the radius. For an entire revolution of 360 degrees, this is equivalent to the arc length for 2π radians. If we represent the angle in radians (A0 in Figure 6.3), the arc length (As) is given by Arc Length = r * Θ, where r is the radius and Θ is the angle in radians.
Solving for the radius using the formula r = Arc Length / Θ, we need to convert the angle from degrees to radians. We know that 180 degrees is equivalent to π radians, so:
144° = (π/180°) * 144° = (π/180) * 144
Now, we can plug in the values and calculate the radius:
88 cm = r * (4π/5)
r = 88 cm / (4π/5)
Substituting the value of π as 22/7, we can simplify the equation to find the radius:
r = 88 * 5 / (4 * 22/7) = 35 cm
The radius of the circle is therefore 35 cm.