The key here is that the circumference of the base of the cone is equal to the arc length of the original sector.
arc-length/10π = 216/360
arc-length = 6π
if radius of cone is r,
2πr = 6π
r = 3
by taking a cross-section of the cone, we get a right-angled triangle with hypotenuse of 5, height of h and base segment of 3
so h^2 + 3^2= 5^2
h = 4
vol of cone = (1/3)π(3^2)(4) = 12π cm^3
A right circular cone is made from of a radius of 5 cm, a central angle of 216 degrees, what is the volume of the cone in cubic cm?
1 answer
1 answer