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Need help

anonymous · Answer

attachment

whpalmer4 · Answer

Do you know the formula for the volume of such a cone?  Find the volume, multiply by the density and you have the target scale reading...

anonymous · Answer

$$V=\frac{1}{3}\pi r^{2} h$$

whpalmer4 · Answer

You'll have to work out the radius from the angle and the height

anonymous · Answer

But I don't have the radius just the apex

anonymous · Answer

Oh okay

whpalmer4 · Answer

Hint: that angle is 2x what you're going to use in your trig formula...

anonymous · Answer

@whpalmer4 I got 6.4 as the radius

whpalmer4 · Answer

I don't think that's correct.  What was your formula?

whpalmer4 · Answer

Did you use 40 degrees or 20 degrees as your angle?

anonymous · Answer

radius = h sin (angle)

anonymous · Answer

I used 40 degrees

whpalmer4 · Answer

No, that's the whole angle, and your triangle only uses half of the angle — look closely at the diagram...

whpalmer4 · Answer

I'm afraid that might not have been your only error, however.

anonymous · Answer

Mkay

whpalmer4 · Answer

isn't it SOHCAHTOA
Sin = Opposite over Hypotenuse
Cos = Adjacent over Hypotenuse
Tan = Opposite over Adjacent
We don't know the hypotenuse here, so sin won't work.  We do know adjacent, however, and we know the angle, so

$$\tan (20 ^\circ) = \frac{r}{10}$$
right?

anonymous · Answer

yeah so the 20 degrees is because I'm only using half of the angle?

whpalmer4 · Answer

Exactly.

whpalmer4 · Answer

and the sneaky SOB who wrote the question stuck in the answer you would get if you made the mistake of using 40 degrees, so you wouldn't even realize your error until you got the graded problem back :-)

anonymous · Answer

Oh okay lolz anyway this helps a lot thanks!

whpalmer4 · Answer

Do you have an answer?

anonymous · Answer

I think it's C

whpalmer4 · Answer

How did you get that?

whpalmer4 · Answer

What was your new, improved value for the radius?

anonymous · Answer

3

whpalmer4 · Answer

Show me your work to find the radius...

anonymous · Answer

tan(20) is equal to 0.36 right?

whpalmer4 · Answer

Yep, approximately.

anonymous · Answer

So wouldn't r = 3.6

whpalmer4 · Answer

Yes, r =3.6  

What do you get for the volume of the cone with r = 3.6 and h = 10?

anonymous · Answer

135.7

whpalmer4 · Answer

Yep.  Now you know the volume of the cone in cm^3.  What is the mass of the gold?

whpalmer4 · Answer

Interesting factoid: all the gold ever mined would make up a cube about 20 or 21 meters on a side...

anonymous · Answer

Sorry my computer powered off for some reason >.<