Draw and solve the diagram of 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 solve this problem, we first need to find the circumference of the circle using the formula:
Circumference = 2 * π * radius
C = 2 * π * 14 cm
C = 28π cm
Next, we need to find the length of the arc of the sector, which is given by:
Arc length = (angle/360) * circumference
Arc length = (120/360) * 28π cm
Arc length = 1/3 * 28π cm
Arc length = 28π/3 cm
Now, when the sector is folded into a cone, the arc length becomes the circumference of the base of the cone. Therefore, we have:
Circumference of the base of the cone = 28π/3 cm
To find the radius of the cone, we can use the formula for the circumference of a circle:
Circumference = 2 * π * radius
Plugging in the values, we get:
28π/3 = 2 * π * radius
14π/3 = π * radius
14/3 = radius
Therefore, the radius of the cone is 14/3 cm or approximately 4.67 cm.