Question

If an arc opposite to central angle of measure 72°was cut from a circle whose radius length 14and bent to from a circle ,then the radius length of the resulted circle

Answer 1

• First, we need to find the arc length of the original circle. The arc length formula is:
L = rtimestheta
where L is the arc length, r is the radius, and
theta is the central angle in radians. We are given that r = 14 and
theta = 72. We need to convert the angle to radians by multiplying it by f racpi180:
theta = 72timesfracpi180 = frac2pi5 Then, we plug in the values into the arc length formula:
L = 14timesfrac2pi5 = frac28pi5
• Next, we need to find the circumference of the new circle. The circumfer-
ence formula is:
C = 2pir′
where C is the circumference and r′ is the radius of the new circle. We know that the arc length of the original circle is equal to the circumference of the new circle, so we can set them equal:
frac28pi5 = 2pir′
• Finally, we need to solve for r′ by dividing both sides by 2
pi:
r′ = fracfrac28pi52pi = frac145 Therefore, the radius of the new circle is 14/5.