A pentagonal pyramid - Math Central

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Question from Alan:

Help me please, I'm pretty stumped here. I guess I'll start with the measurements I do have.
The pentagon base of the pyramid is inscribed in an eight inch circle, giving each side the
measurement of 4 & 5/8 inches.

I have two glass billets measuring 5"x10"x3/4"
If I did the math right I need the form to hold about 75 cubic inches.

What does the height of the pyramid need to be to hold the volume of the two billets? (note: the billets
will be broken into smaller pieces to actually fit into the form.)

Hi Alan.

The volume of a pyramid formed from a regular pentagon base is

Where a is the length of a side and h is the height.

That volume equals the volume of your two billets: V = 2 (5 x 10 x 0.75) = 75 cubic inches, as you said.

So set these equal to one another and solve for h to get the corresponding height.

Hope this helps,
Stephen La Rocque.

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