<![CDATA[Math Is Fun Forum / Help]]> 2007-02-21T01:27:11Z FluxBB https://www.mathisfunforum.com/viewtopic.php?id=6126 <![CDATA[Re: Help]]> I'm assuming the text is meant to say

This figure is the base of a cone that is 8 inches tall.
What is the volume of the cone? Dimensions are in inches.

It's a curious property of cones that no matter how irregularly shaped its base is, its volume can always be worked out by (basearea x height)/3.

So if we can work out the area of that base, then the rest is easy.
The base is composed of a right-angled triangle and a sector of a circle.

Triangle: (8*12)/2 = 48.
Sector: π*8² * (50/360) = 80π/9.

Therefore, the total area of the base is 48 + 80π/9, which is ~ 75.9 square inches.

From here, we just need to multiply by the height and divide by 3, which gives a final area of:
(8/3)(48 + 80π/9) cubic inches if you're being exact, or ~202 cubic inches if you're approximating.

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https://www.mathisfunforum.com/profile.php?id=641 2007-02-21T01:27:11Z https://www.mathisfunforum.com/viewtopic.php?pid=60025#p60025
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https://www.mathisfunforum.com/profile.php?id=5209 2007-02-21T00:52:12Z https://www.mathisfunforum.com/viewtopic.php?pid=60024#p60024