Bryan P. answered • 05/11/16
Tutor
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Math, Science & Test Prep
Mohamed,
I believe your question is missing some critical information. Since I cannot draw in this editor, I'll describe the picture that you should draw to aid in your understanding. For clarity, a sector is like a piece of pie, cut from the center to the outer edge of the circle. The central angle of this sector is dependent only upon how much pie you want. There is no defined angle for a sector.
Draw a circle, any radius big enough to make notes on, and pick two points on the circumference to label as A and B. Now here's where we need more information. If you cut out the sector you have drawn and curl A and B together to make a cone, you will see that the slant of the cone matches the radius of the original circle you drew. So in this case that is given as 24 cm. But everything else about this cone is dependent upon where you chose to put A and B on the circle.
I appears that you may have pasted the question in from another source where you may find that information. It could be given as the arc length from A to B, or possibly the central angle between A and B. I will lay out the process for you in the hopes that you can find that information.
Knowing that the arc length from A to B on the original circle becomes the circumference of the cone, I use the following equation:
Ccone = 2πrcone = arcAB = 2πrcircle • 360/θ = 2π(24)360/θ, where θ is the central angle from A to B on the original circle.
Using the second and last parts, we get rcone = 8640/θ.
Now if you draw a cone, you see that the slant and the radius form a right triangle with the height of the cone. So we use Pythagorean theorem to solve for height:
hcone = √(242 - (8640/θ)2)
Now use the height and radius to find the volume by V = πr2h/3.
I hope that helps.
