karentao77 said:
a sector of a circle with radius 5 cm and an angle of π/3 subtended at the centre is cut out of cardboard. it is then curved around to form a cone. Find its exact volume.
answer: (125 √35π) /648
Volume of a cone is 1/3
πr
2h
l=r@ (r as in the radius of the sector)
l= 5
π/3
Since the length of the arc is circumference then:
5
π/3 = 2πr (r as in the radius of the circle at the base of the cone)
.: r=5/6
for the height: using pythagorus (the 5 which was the radius of the sector becomes the slanted side of the cone, and the 5/6 is the radius of the circle at the base of the cone) [if you don't fully understand this, drawing a diagram helps
]
h=5
2 - (5/6)
2
=
√(875/36)
which simplifies to (5
√35)/6
Now to answer the question
Volume: 1/3
πr
2h
1/3 *
π * 25/36 *(5
√35)/6
=(125 √35
π) /648 units
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