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March 31, 2015

March 31, 2015

Posted by **hodna** on Sunday, April 11, 2010 at 9:40pm.

and tapes the straight edges together to form a cone. Given that the sector radius is 12

cm, find the height and volume of this paper cone.

- math -
**Reiny**, Sunday, April 11, 2010 at 10:35pmThe circumference of the whole circle from which you cut the sector is 2π(12) = 24π cm

so using ratios to find the circumference of the sector:

120/360 = x/24π

x = 8π

That becomes the circumference of the base of the cone

for its radius r :

2πr = 8π

r = 4 cm

The radius of the original sector becomes the slant side of the cone

so h^2 + 4^2 = 12^2

h = √128 = 8√2

vol = πr^2h/3 = π(4)^2(8√2)/3 = (128π√2)/3 cm^3 or appr. 189.563

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