Calculate the slant height for the given cone. Round to the nearest tenth.

Question

anonymous · Answer

attachment

compassionate · Answer

Do you know the formula for the height of a cone?

anonymous · Answer

Nope.. I'm completely lost ;_;

e.mccormick · Answer

Actually, it is slant height, so you can just look at the right triangle there.  Know your triangle formulas?

compassionate · Answer

$$Height = 3\frac{ V }{ \pi r^2 }$$

Where V = Volume
pi = 3.14
And radii = 4 (Since the diameter is 8, and radius = diameter/2)

mathstudent55 · Answer

You need the Pythagorean theorem.

e.mccormick · Answer

Comp, what does that have to do with slant height?

compassionate · Answer

Whoops. I misread your question. Slant Height is different.

anonymous · Answer

I'm so confused ._.

e.mccormick · Answer

Yep. The Pythagorean Theorem.  Just be careful with the leg lengths.  They made one number a tad bit tricky.

mathstudent55 · Answer

|dw:1425337661251:dw|

e.mccormick · Answer

Sam, just forget what Comp typed in at first...  they were thinking about height and volume, not the slant height.  Jist look at the pic math student drew.

mathstudent55 · Answer

The slant height is the hypotenuse of a right triangle.
You know the lengths of the legs. One leg is the height of the cone, and the other leg is the radius of the cone, which is half the diameter.

compassionate · Answer

Well, you could assume by rearranging the Pythagorean theorum that $$SH = \sqrt{r^2 + h^2}$$

anonymous · Answer

??! Am I overthinking this or...?

e.mccormick · Answer

Well, know your Pythag?  $a^2+b^2=c^2$?

e.mccormick · Answer

For any right triangle, the square of the hypotenuse is equal to the sum of the squares of the legs.
|dw:1425338206567:dw|
$a^2+b^2=c^2$

e.mccormick · Answer

As you can see, that can be applied to this problem to make the drawing mathstudent55 did:
|dw:1425338305132:dw|

anonymous · Answer

So, what do I do? {math especially angles and triangles and all that fun stuff I can never figure out}

e.mccormick · Answer

Well, what is your height from your diagram?

anonymous · Answer

9 cm

e.mccormick · Answer

Good.  Now, what is your base leg lenth?

anonymous · Answer

8 cm..?

e.mccormick · Answer

Not quite.  It is related to that, but that is the diameter.  You want just the radius.

anonymous · Answer

oh 4

e.mccormick · Answer

Good!

|dw:1425338765680:dw|
OK, so, put those into the formula.

anonymous · Answer

Umm..

anonymous · Answer

like 9^2 + 4^2?

e.mccormick · Answer

YES!

e.mccormick · Answer

What you get will be the square of the hypotenuse, or the square of the slant height.  So all that is left after squaring and adding is finding the root.

anonymous · Answer

wait so like 81 + 16 = 97 then you find the root?

e.mccormick · Answer

Yes.  That is it.  $\sqrt{97}$ will be it.

anonymous · Answer

What do you do to get the square root again?

e.mccormick · Answer

Well, it says to round to the nearest 10th.  So I would use a calculator and round off.

anonymous · Answer

ok thanks

anonymous · Answer

so 10.2 ??

anonymous · Answer

@e.mccormick

anonymous · Answer

actually 9.8

e.mccormick · Answer

10*10 = 100, so 10^2 would be too high.  9^2=81, so too low.  It will be some number between 9 and 10.

anonymous · Answer

Can I tag you in a couple more questions? It shouldn't take as long..

e.mccormick · Answer

Yah, 9.8 is to the nearest 10th.

e.mccormick · Answer

Well, I am getting some fun reports to deal with at the moment...