Question to Find the Radius of the Circle

Topic : Geometrical Figures

Question : A cone is formed with an arc length AB equal to 20 cm. As the cone is formed from a sector of a circle with angle 72 degrees, determine
a) the radius of the circle from which the sector is taken, and
b) the radius of the base of the cone formed by sector ABC

ANSWER:

(a) Step1: Given, Arc Length=20cm
Angle = 72 degrees
Required = Radius( r )
Step2: Circumference = 2Pi*r
arc length = (x/360 degrees) * 2Pi*r
Step3:Putting the values
20 = (72/360)*2Pi*r --------[pi=22/7=3.14]
r = 15.915 cm
1(b) Step1: Given, Same as 1(a)
Required =the radius of the base of the cone
Step2: circumference = 2Pi*r base of cone = circumference
Step3:Putting the values
20 cm = 2Pi*r
r = 10/Pi
r = 3.18 cm

Question to Find Arc Length of a Circle

Topic : Arc Length

Question : If a Circle has 11cm radius, Find the Length of an arc in the Circle.

Solution :

We have a Formula,
measure of arc/360 = arc length/circumference

90/360 = arc length/2πr = arc length/2π(11)

90/360 = arc length/22π


Hence the arc length = 22π * 90/360 = 11π/2 = 5.5π cm