Question

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

Answer 1

@amistre64 @TheSmartOne

Answer 2

@ParthKohli @iambatman

Answer 3

i never understood with question .... unless its half a cone

Answer 4

how do you form a cone from a sector?

Answer 5

and what is a diameter of a sector?

Answer 6

idk too. thats why i post this question.

Answer 7

I don't think you can

Answer 8

segment is a pizza slice

sector is cutting off the edge of a circle .... right?

Answer 9

wait, can you explain this yahoo answer amistre..

Answer 10

If the diameter of the sector is 72 inches, then its radius, which is also the slant height of the cone, is 36 inches. The circumference of that complete circle would have been C = πd or C = 72π.

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)

V = 441π√95 <==ANSWER

V = 13,603.62 in³ <==decimal ANSWER

Answer 11

ahh ok, then yeah, that makes more sense

Answer 12

thats roughly sector of 7pi/6

Answer 13

i cant understand this part:
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.

Answer 14

seems welsh is on a good track

Answer 15

what is the length of the arc of the associated sector?