A 240 degree sectors of a circle of a radius 14cm is bent to form a cone.find the radius of the base of the cone and it vertical angle

length of arc of base = (240/360) * 2 * pi * 14 = (2/3) * 28 pi = 58.6 cm

that is the circumference of the base of the cone
2 pi Rcone = 58.6
Rcone = 9.33 cm
slant height = 14 cm
sin (Theta/2) = 9.33 /14
Theta/2 = 41.7
Theta = 83.6 deg

Did you know?

Did you know that a 240-degree sector of a circle with a radius of 14cm can be bent to form a cone? To find the radius of the base of the cone, we can use the formula for the circumference of a circle. Since the circle is missing a 120-degree angle, we can find the missing circumference by calculating (360 - 120) / 360 = 240 / 360 = 2/3. Therefore, the circumference of the base of the cone is 2/3 of the circumference of the original circle. We can find the circumference of the circle using the formula 2 * π * r. By substituting the given radius of 14cm, we get 2 * 3.14 * 14 = 87.92 cm. Now, finding 2/3 of this value, we get 2/3 * 87.92 = 58.61 cm. Therefore, the radius of the base of the cone is approximately 58.61 cm. As for the cone's vertical angle, it would be the angle formed at the apex of the cone by joining the center of the circle with the two endpoints of the original sector.