A sector of radius 14 cm subtend an angle of 240 degree at the center of the circle is bent to form a cone calculate the base radius of the cone

major arc/(28π) = 240/360 = 2/3

major arc = 28π(2/3) = 56π/3
This becomes the circumference of the base of the cone
let the radius be r
2πr = 56π/3
r = 28/3
state your conclusion using the correct units

Well, if I were to bend a sector of a circle into a cone, I think the real question is: would the cone then develop a fear of clowns? But let's set that aside for now and focus on the math.

The circumference of the circle from which the sector is taken can be calculated using the formula:
C = 2πr

In this case, the radius of the circle is given as 14 cm. So, we can plug it into the formula:
C = 2π(14)
C ≈ 87.9646 cm (approximately)

Since the sector subtends an angle of 240 degrees, it represents about 240/360 (or 2/3) of the circumference of the circle.

Now, let's calculate the length of the arc representing the sector:
Arc = (2/3) * C
Arc ≈ (2/3) * 87.9646 cm
Arc ≈ 58.6427 cm (approximately)

The length of the arc will become the circumference of the base of the cone. The formula for the circumference of a cone's base is:
Cone Base Circumference = 2πr

We can equate this to our arc length and solve for the cone's base radius (r):
58.6427 cm = 2πr

Now, we can solve for r:
r = 58.6427 / (2π)
r ≈ 9.3209 cm (approximately)

So, the base radius of the cone, formed by bending the sector, is approximately 9.3209 cm.

To calculate the base radius of the cone, we first need to determine the circumference of the circle that corresponds to the sector.

The formula to calculate the circumference of a circle is:
C = 2πr

Given that the radius of the sector is 14 cm, the circumference of the circle is:
C = 2π(14) = 28π cm

Since the sector subtends an angle of 240 degrees at the center, it forms 2/3 of the entire circle (240/360 = 2/3).

To calculate the base circumference of the cone, we need to find 2/3 of the circumference of the circle:
Base Circumference of Cone = (2/3) * 28π
= 56/3π cm

We know that the circumference of a circle is related to the base radius of a cone by the formula:
Cone Base Circumference = 2πr

Setting the base circumference of the cone equal to 56/3π cm, we can solve for the base radius:
2πr = 56/3π

Dividing both sides by 2π:
r = (56/3π) / (2π)

Simplifying:
r = 28/3

Therefore, the base radius of the cone is 28/3 cm.

To find the base radius of the cone formed by bending a sector of a circle, we need to use the information provided about the sector.

First, let's calculate the circumference of the circle from which the sector is formed. The formula for the circumference of a circle is given by C = 2πr, where C is the circumference and r is the radius.

Given that the radius of the circle is 14 cm, we can calculate the circumference as follows:

C = 2π(14)
C = 28π cm

Next, we need to find the circumference of the cone's base, which is equal to the circumference of the circle. This is because bending the sector of the circle forms the base of the cone, and the length of the bent part becomes the circumference of the base.

The formula for the circumference of a circle is also applicable to the base of the cone:

Cone base circumference = 28π cm

To find the radius of the cone, we need to use the formula for the circumference of a circle and rearrange it to solve for the radius:

Cone base circumference = 2πr

Substituting the known value for the circumference of the cone base:

28π = 2πr

Canceling out the common factor of 2π:

14 = r

Therefore, the base radius of the cone is 14 cm.