A sector with radius 10 and central angle $45^\circ$ is to be made into a right circular cone. Find the volume of the cone.
The slant height of the cone will be = 10
The circumference of the cone = 2pi *10 (45/360) = 2.25 pi = 2pi r
The radius of the cone = 2.25/2 = 9/8 =1.125
The height of the cone = sqrt (10^2 -1.125^2 )
The volume of the cone =
pi * r^2 * height / 3 =
pi * (1.125)^2 * sqrt (10^2 - 1.125^2) / 3 ≈ 13.17 units^3
A sector with a radius of 10 and a central angle of 45º is to be made into a right circular cone. Find the volume of the cone.
("central angle of 45º " means that a sector of 45º is cut out and the remaining (larger) sector is used to make a cone.)
Circle radius = 10 (this is also the slant height of a cone)
Cone radius = 10(315/360) r = 8.75
Cone height h = sqrt(102 - 8.752) = 4.841229183
Cone volume V = pi * r2 * h/3 V ≈ 388.15 square units
The question calls for the right cone; let's check if it's a right cone.
102 = 8.752 + 4.8412291832
100 = 100 correct!!!