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

Answer 1

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.