Asked by simar
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?
Answers
Answered by
Reiny
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
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
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