A sector of a circle of radius 14cm which subtends angle 120° at the centre is folded into a cone find the radius of the cone
To find the radius of the cone, we first need to find the circumference of the sector of the circle.
Circumference of the sector = (120/360) x 2π x 14 cm
= (1/3) x 2 x 3.1416 x 14 cm
= 29.3864 cm
Now, when the sector is folded into a cone, the circumference becomes the base circumference of the cone. Since the circumference of a circle is equal to 2πr, we can find the radius of the cone using the formula:
2πr = 29.3864
r = 29.3864 / (2 x 3.1416)
r ≈ 4.68 cm
Therefore, the radius of the cone is approximately 4.68 cm.