Caitlyn made a teepee for a class project. Her teepee has a diameter of 6 feet. The angle the side of the teepee made with the ground was 65 degrees. What was the volume of the teepee? Round your answer to the nearest hundredth.

Question

anonymous · Answer

If only the angle was 60 degrees...Dang it...

anonymous · Answer

well, do you at least know a formula on how to do it?

anonymous · Answer

Can't say I do for this one. 65 degrees is an unusual angle to work with. I'll think it through some more.

anonymous · Answer

okay thank you

anonymous · Answer

No luck so far. Still trying.

anonymous · Answer

Found a solution! Hold on.

anonymous · Answer

Okay, so we know that the radius of this circle is 3; that is the length of the shortest leg of a right triangle. 

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I'm trying to solve for the height, the bottom of that triangle. Call it 'y'. I use to tangent to get there, because: tan = opposite / adjacent. So then, tan 65 = y / 3. We know that this is the same as saying y = 3 tan 65. So then, y = 6.43. 

This is the height; we can now solve for the volume of the cone.

V = (pi*(r)^2)*(h/3)
V = (pi*(3)^2)*(6.43/3)
V = (9pi)(6.43/3) = 60.60 feet cubed.

That is a beautiful problem. Thank you for giving me a challenge.

anonymous · Answer

Oh My Gosh THANK YOU SO MUCH YOU ARE SO AMAZING

anonymous · Answer

Ha-ha! Absolutely! ^_^