A paper cone has a base diameter of 8cm and a height of 3cm if the cone is cut and opened out into the sector of a circle what is the angle of the sector
To find the angle of the sector, we need to calculate the circumference of the base of the cone.
The circumference of a circle can be calculated using the formula C = π * d, where C is the circumference and d is the diameter.
Given that the base diameter of the cone is 8 cm, we can calculate the circumference of the base:
C = π * 8cm
C ≈ 25.13 cm
When the cone is cut and opened out into the sector, the circumference of the base forms the arc length of the sector. We can denote this length as S.
Since circumference = sector angle * radius (C = θ * r), we can rearrange the formula to solve for the sector angle:
θ = C / r
θ = 25.13 cm / 3cm
θ ≈ 8.38 radians
So, the angle of the sector is approximately 8.38 radians.