A paper cone has a base diameter of 8cm and a height of 3 . If a cone is cut and opened out into a sector of a circle what is the angle of a sector
To find the angle of the sector formed when the cone is cut and opened out, we need to first calculate the slant height of the cone.
Given that the base diameter of the cone is 8cm, the radius (r) of the cone is half of the diameter, so r = 8/2 = 4cm.
Using the Pythagorean theorem, we can calculate the slant height (l) of the cone:
l = √(r^2 + h^2)
l = √(4^2 + 3^2)
l = √(16 + 9)
l = √25
l = 5cm
Now that we have the slant height of the cone, we can calculate the circumference of the base of the cone:
Circumference = 2πr
Circumference = 2π(4)
Circumference = 8π cm
The sector is formed by cutting and opening out the cone, which means that the arc length of the sector will be equal to the circumference of the base of the cone. Therefore, the angle of the sector can be calculated using the formula for the angle of a sector of a circle:
Angle (θ) = (arc length / circumference) * 360°
Angle (θ) = (8π / 8π) * 360°
Angle (θ) = 360°
So, the angle of the sector formed when the cone is cut and opened out is 360°.