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IB HL Math Portfolio - Volumes of Cones (Type III)
The first 200 words of this essay...
In this assignment, I will use WinPlot, a graphing display program.
1. Find an expression for the volume of the cone in terms of r and ?.
The formula for the volume of a cone is: V = 1/3 x height x base area
To find the base area, we must find the radius of the base.
The circumference of the base of the cone = the length of arc ABC
2? ? rbase = r?
rbase = r? / (2?).
The area of the base can therefore be calculated:
Abase = ? ? rbase 2 = ? ? ( r? / (2?))2
Next, we must find the height of the cone, h.
Notice that for the cone, h rbase r is a right angled triangle, with r as the hypotenuse.
Therefore, using the Pythagorean Theorem, we can find h.
r2 = h2 + R2
r2 = h2 + (r?/2?)2
h2 = r2 - (r?/2?)2
h = ? [r2 - (r2?2/4?2)]
Therefore, substituting the values for rbase
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