Find the volume of a cone formed from a sector of diameter 72 inches and a central angle 7pi/6.

Question

badmood · Answer

V = 441π√95 

V = 13,603.62 in³

anonymous · Answer

how did you get that?

badmood · Answer

yahoo.com

badmood · Answer

i had a long thing to read

badmood · Answer

if i show u how i got it if u dont mind

anonymous · Answer

i dont understand, i want simpleton :D

badmood · Answer

If the sector had a central angle of 7π/6, then the length of its arc is (7π/6)/(2π) * 72π = (7/12) * 72π = 42π 

42π is also the circumference of the base of the cone to be formed. 

If 42π is the circumference of the base of the cone, then its diameter is 42, so its radius is 21 inches. 

If its radius is 21 inches and its slant height is 36 inches, then find the cone's height: 

a² + b² = c² 

radius² + cone's height² = slant height² 

21² + h² = 36² 

441 + h² = 1296 

h² = 855 

h = 3√95 inches 


volume = ⅓ area of base x height 

V = ⅓ πr²h 

V = ⅓ π(21)²(3√95)

badmood · Answer

understand now

anonymous · Answer

(7π/6)/(2π) * 72π = (7/12) * 72π = 42π , idont get this