Aran moved a cone-shaped pile of sand that had a height of 6 ft and a radius of 3 ft. He used all of the sand to fill a cylindrical pit with a radius of 6 ft.

How high did the sand reach in the pit?
Use 3.14 to approximate pi and express your final answer in tenths.

Question

Aran moved a cone-shaped pile of sand that had a height of 6 ft and a radius of 3 ft. He used all of the sand to fill a cylindrical pit with a radius of 6 ft.
 
How high did the sand reach in the pit?
Use 3.14 to approximate pi and express your final answer in tenths.

mathstudent55 · Answer

You need the formulas for the volumes of a cone and a cylinder.

anonymous · Answer

3.14xr^2xh/3

anonymous · Answer

and 3.14xr^2xh

mathstudent55 · Answer

Correct. Here they are written in LaTeX which makes it easier to understand:

$\Large V_{cone} = \dfrac{1}{3} \pi r^2 h$

$\Large V_{cylinder} =  \pi r^2 h$

mathstudent55 · Answer

Now compare the formulas.
If you have a cone and a cylinder, and they both have the same radius of the base and the same height, how do the volumes compare?

anonymous · Answer

We don't know the height of the cylinder...Right/ I really don't understand

mathstudent55 · Answer

Let me explain better what I was asking above.
I'm not talking about your problem now.
This is just in general.
Let's say you have a cone and a cylinder.
The cone and the cylinder have the same radius. The cone and the cylinder have the same height.
What will be the difference in their volumes?
To answer this question, just look at the formulas for the volumes.
What is the only difference you notice between the volume formulas?

anonymous · Answer

1/3?

mathstudent55 · Answer

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mathstudent55 · Answer

Exactly. The only difference is the 1/3 in the cone's volume formula.
That means for the same height and radius of a cone and a cylinder, the cone's volume is 1/3 the size of the cylinder's volume.

mathstudent55 · Answer

Ok. Now let's deal with your problem.

mathstudent55 · Answer

Since you know the formula for the volume of a cone, you can use it to find the volume of the original pile of sand, which is a cone with given radius and height.

anonymous · Answer

169.65?

mathstudent55 · Answer

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mathstudent55 · Answer

Great.
Now you need the formula for the volume of a cylinder.
Write the formula with the info you know, r = 6, leave the height as h, and set it equal to the volume of the cone you just found above.
Then solve for h.

anonymous · Answer

3.14*6^2*h
3.14*36*h
113.04*h

anonymous · Answer

169.65=113.04*h

anonymous · Answer

169.65-113.04=56.61=h?

anonymous · Answer

Nope it's wrong ummm I don't know...

mathstudent55 · Answer

Wait. Just one question.
In finding the volume of the cone, did you divide by 3 like the formula requires?

mathstudent55 · Answer

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