Saturday

April 19, 2014

April 19, 2014

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

**Related Questions**

Geometry - Infinitely many different sectors can be cut from a circular piece of...

geometry - 11. Infinitely many different sectors can be cut from a circular ...

calculus - A paper cone is to be formed by starting with a disk of radius 9cm, ...

calculus - A paper cone is to be formed by starting with a disk of radius 9cm, ...

calculus - A paper cone is to be formed by starting with a disk of radius 9cm, ...

CALCULUS - A cone shaped paper drinking cup is to be made from a circular piece ...

Math - Cone Problem Beginning with a circular piece of paper with a 4- inch ...

PreCalculus - Cone Problem Beginning with a circular piece of paper with a 4- ...

Math - I already posted this, but wanted to say that I have the answers and it ...

Math - A cone is constructed by cutting a sector from a circular sheet of metal ...