I am trying to work out the volume of a Pentagonal Pyramid with a hight of 32cm, and side lengths of 15cm's. That is all the information i have and im stuck on the actual volume. Anyone able to help at all?

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- Nov 14th 2010, 08:04 AMcalisthulePentagonal Pyramid Volume help
I am trying to work out the volume of a Pentagonal Pyramid with a hight of 32cm, and side lengths of 15cm's. That is all the information i have and im stuck on the actual volume. Anyone able to help at all?

- Nov 14th 2010, 08:11 AMWilmer
- Nov 14th 2010, 08:16 AMcalisthule
ive tried using google, but its no help to me :S... Im a drama student but going to be making some props for a play, but my lecturer wants me to be specific with everything i make, and i need to know the area of the thing :S. Going to be filling it up with fake blood but i dont want to get too much or too little :S, and i need to buy it tmw, and i will be at uni on tuesday as they are going to be building it then so we need to know the exact amount before it is built :S.

Anyone able to help? - Nov 14th 2010, 08:20 AMUnknown008
The volume of any pyramid is given by:

$\displaystyle V = \dfrac13 \times \text{base area} \times \text{height}$

Find the area of the base.

Make a sketch. I assume that it's a regular pentagon, which means you can divide it into 5 equal triangles of apex 72 degrees at the centre of the pentagon. Can you work out it's area knowing the angle and 1 side? (Hint: You can divide each triangle into two, giving two right angled triangles with one side as 15/2 and an angle of 76/2 and use a trigonometric ratio to find the height, then the area)