Posted by **Lucas** on Tuesday, May 15, 2012 at 3:20am.

The sector shown is formed into a cone by joining its two radii. Calculate the volume of the cone correct to the nearest whole number.

It shows a diagram with a 240 degree sector or two-thirds of a circle with a radius of 12 cm.

How do I do this?

Thank you so much

- geometry -
**Reiny**, Tuesday, May 15, 2012 at 9:07am
Sometimes it helps to have an actual model of your problem.

Take a piece of paper and cut out a sector approximating your given sector.

Form it into a cone.

You will see that the radius of the sector becomes the "slant height" of the cone, and the arc length of the sector becomes the circumference of the base of the cone.

So, let's find the radius of the cone:

The arc length of our sector would be 240/360 of the circumference of the circle from which the sector was obtained.

so (240/36)( 24π) = 16π

then for the base of the cone

2πr = 16π

r = 8

Now we can find the height of the cone:

h^2 + 8^2 = 12^2

h = √80

Volume of cone = (1/3) base x height

= (1/3)(64π)(√80)

= appr. 599 to the nearest whole number

## Answer This Question

## 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 ...
- Geometry - A piece of paper in the form of a sector of a circle of radius 15 cm ...
- Cranborne - In the diagram AOBP is the major sector of a circle centre O.BO=8cm...
- 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, ...
- math - Dana takes a sheet of paper, cuts a 120-degree circular sector from it, ...
- Maths - The angle of a sector of a circle with radius 42cm is 120 degree.if the ...
- math - A cone is made from the figure shown by joining the straight edges and ...

More Related Questions