A cone formed by bending a sector of a circle having an angle of 288 degrees. Find the radius of the base of the cone if the diameter of the circle is 18cm

288/360 * 9

To find the radius of the base of the cone, we need to use the formula for the circumference of a circle and the relationship between the circumference of a circle and the circumference of the sector.

Let's start by finding the circumference of the sector. We know that the angle of the sector is 288 degrees, which is 288/360 = 4/5 of a full circle. Since the diameter of the circle is given as 18 cm, the radius of the circle is half of the diameter, which is 18/2 = 9 cm.

The circumference of a full circle is given by the formula C = 2πr, where r is the radius. So, the circumference of the circle is C = 2π * 9 = 18π cm.

Since the sector forms a cone, its arc length (circumference) is equal to the circumference of the base of the cone, which is the circumference of the circle. Therefore, the arc length of the sector is also 18π cm.

Now, let's find the circumference of the base of the cone.

The circumference of a circle (the base of the cone) is given by the formula C = 2πr, where r is the radius of the base of the cone. We want to find the radius, so let's solve this equation for r.

We have 18π = 2πr, divide both sides of the equation by 2π, we get:

r = (18π) / (2π) = 9 cm.

Therefore, the radius of the base of the cone is 9 cm.