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.

The answer is 0.5 but I do not understand how to get this answer, some help would be appreciated :)

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.

The answer is 0.5 but I do not understand how to get this answer, some help would be appreciated :)

genericnoodles · Answer

I dont need help asap, but sometime today would be awesome!

wolfe8 · Answer

Hey welcome to OpenStudy. Do you know the volume formulas for cones and cylinders?

genericnoodles · Answer

Yes!

wolfe8 · Answer

Alright cool. So tell me what you understand or don't understand and I'll walk you through this

genericnoodles · Answer

Thank you so much! I did the formula for the cone-shaped pile and that was fairly easy, I just do not understand how i'm supposed to tell how much sand filled up the cylinder if they do not give me the height, nor volume of it.

wolfe8 · Answer

Ah alright. Ok so the amount of sand in that cone shape will be the same as in the cylinder, right? So you equate this volume with the cylinder formula. What is the only unknown parameter you have after that?

genericnoodles · Answer

The height of the cylinder?

wolfe8 · Answer

Yup! And that is the question. So if you solve the equation for height you're done.

genericnoodles · Answer

Awesome! Im going to do that real quick.

genericnoodles · Answer

Thank you for the help, this was a pretty confusing question for me :D

wolfe8 · Answer

Yup I'll be here until you can get it right.

genericnoodles · Answer

Before I do this, I got 55.9548 as the volume for the cone, is that correct? I multiplied it by 0.33, then pi.

wolfe8 · Answer

Hmm close but not quite. Can you show me what you did?

genericnoodles · Answer

Of course! $$v=1/3(3.14)\times(54)$$

genericnoodles · Answer

I did use 0.33 as 1/3, could that be the problem?

wolfe8 · Answer

Most probably. You can just do 54/3 :)

genericnoodles · Answer

I think I understand it now, just to be sure, Ill show you my equation. $$56.52=(3.14)36h$$
then I divided 56.52 by the 113.04 and got 0.5! You've been an awesome help, and as soon as I figure out how to medal you I will do so xD

wolfe8 · Answer

Yup yup. Good job! :)

So if it confused you, notice that you are moving a cone of sand into a cylinder. You should have the same amount of sand before and after so the volume should be the same. Only the shape changes. Setting up equations with this info should make it clear what you have to do.