Find the volume and the total surface area of a regular tetrahedron in which the measure of one edge is 10m.

Question

lastdaywork · Answer

See these formulas; they might come handy in future - http://en.wikipedia.org/wiki/Tetrahedron#Regular_tetrahedron

kainui · Answer

This is a very fun problem to solve because you can perfectly fit a regular tetrahedron inside a cube and use a little trigonometry to figure out what you need. The cube makes it a lot easier to visualize.|dw:1391765689820:dw|

anonymous · Answer

but i don't know how to solve it :(

anonymous · Answer

but in your figure why did you include the cube?

kainui · Answer

Since it's a regular shape, that means all the sides are exactly the same. So if you can see in this picture: |dw:1391765774836:dw| http://upload.wikimedia.org/wikipedia/commons/2/21/Tetrahedron-3-3D-balls.png It has 4 sides and all 4 sides are equilateral triangles.

anonymous · Answer

so how to solve it? can you help me?

kainui · Answer

That's what I'm doing right now. Let's start with the surface area and try to find that. What's your best guess? I've already given you some information on that. 

Total surface area is just the sum of all the areas of each face. If there are 4 faces and each face is an equilateral triangle... Well just find the surface area of one of those faces and multiply by the total number... That's the total surface area. Volume will be next, but one thing at a time.

anonymous · Answer

the formula for the total surface area for tetrahedron is nps^2 divided by 4 tan9180 over n)^2

kainui · Answer

Did you come up with that yourself?

anonymous · Answer

n is the number of sides so we have 4 sides and s is the length of an edge so its 10m.

anonymous · Answer

no its in my reference book

anonymous · Answer

and p is the mnber of polgon

kainui · Answer

So what's the issue then, seems like you just need to plug and chug if you already have formulas? I can show you where the formulas come from, but I won't plug in numbers for you.

anonymous · Answer

hmmm im just a bit confused so can you please help me?

kainui · Answer

That's what I have done. Start from the top and give me a guess based off of the help I've already given.