Find in term of pi the curved surface area of a cone with circular base diameter 10 cm and height of 12 cm .if the cone that question below is made of paper and the paper is flattened or out into the sector of a circle what is the angle of the sector
The radius of the circular base is 5 cm (half of the diameter) and the slant height of the cone can be found using the Pythagorean theorem:
s = sqrt(5^2 + 12^2) = 13 cm
The curved surface area of a cone is given by:
CSA = πrs
where r is the radius of the circular base and s is the slant height.
Plugging in the values, we get:
CSA = π(5)(13) = 65π cm^2
To find the angle of the sector into which the paper can be flattened, we need to use the lateral surface area of the cone, which is the curved surface area without the circular base.
The lateral surface area of a cone is given by:
LSA = πr(s)
where s is still the slant height and r is now the radius of the base of the sector.
Since the lateral surface area of the cone and the area of the sector will be the same (since the paper is flattened into the sector), we have:
LSA of cone = area of sector
πrs = (1/2) r^2 θ
Simplifying, we get:
2s = rθ
Plugging in the values for s and r, we get:
2(13) = 5θ
Solving for θ, we get:
θ = 52.8 degrees (rounded to one decimal place)
Therefore, the angle of the sector into which the paper can be flattened is approximately 52.8 degrees.