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Posted by Subhotosh Khan on October 08, 2002 at 12:09:22:

In Reply to: other questions posted by Kurt on October 08, 2002 at 11:47:36:

: I understand what needs to be done, Mr K, but can't finish it.
: Too many things I haven't seen before.

: :mAOB = T
: I understand "AOB", but what is T? degrees, like 75 degrees? Yes
: What does "m" mean? It is short of "measure of" or "value of" angle AOB

: :From that you can get the area of the base(A_1)
: Why do I need to get the area? Look below

: :volume of small cone (V_1)=1/3*R*A
: where does that come from? V = (pi r^2 h) / 3, is it not? In this case A = pi * r^2 .... and h = R (the radius of the circle you started with) so we are talking about the same thing
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Assume mAOB = T (in radians)

So chord AB = R * T (definition of angle)

So the circumference of the base of the small cone

2* pi * r = R * T ? (r = radius of the circular base of the small cone)

r = R * T/(2*pi)

V_1 = (pi)* r^2 * h / 3

= (pi)* [R * T/(2*pi)]^2 * R / 3

= R^3/(12*pi) * T^2

Similarly find V_2

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