A pile of gravel spread over a driveway?formula?

Question

I need to know if i have a gravel pile with a base of 5 ft and a height of 10 ft and it needs to be spread over a driveway 10x 4 ft 2 inches deep will i have enough gravel? How do i do this math problem?

I was told by my math teacher to use a cylinder then a funnel formula but i wasnt sure how to apply it.

Answer 1

First, you find the volume of your pile of gravel, then you find the volume of the layer you want to spread over the driveway - if the first volume is ≥ the second, you have enough gravel, otherwise you don't. Technically this problem is underspecified, since you aren't told what shape the pile of gravel is, but we shall assume that it's a cone, and that the dimension given for the base is the diameter. This means the cone radius is 2.5 ft. The volume of a cone is given by V=πr²h/3, which gives us V=π(2.5 ft)²*10 ft/3 ≈ 65.4498 ft³. The volume of gravel needed to cover the driveway is 10 ft * 4 ft * 1/6 ft = 40/6 ft ≈ 6.6667 ft³. Therefore, you have more than enough gravel to cover the driveway.

Edit: didn't see the second part of your question - the funnel formula is just the cone formula we just used. A cylinder will have a volume of πr²h, i.e. 3 times the volume of a cone with the same base and height. It sounds as though your teacher is telling you to assume various shapes of the pile to place upper and lower bound on the amount of gravel in it - good strategy. Of course, since the cone gives us a lower bound well in excess of the required quantity of gravel, there's really no need to compute the upper bound to know for certain that you have enough.

Answer 2

You need to measure that pile again. There is no way. And if it really is 10' high, you have got WAY too much gravel.

Oh yeah, and by the way you need at LEAST 6" of gravel for a driveway if you plan on having vehicular traffic on it. If you want heavy traffic, e.g. trucks on it you'll need 8-12" thick base.

Answer 3

Base? if radius (or halfway across the bottom of your pile measures 5 ft, then -
You roughly have:
1.) A cone which contains 1/3(5π)ft2*10ft = 822.47 cu. ft of gravel

2.) a cube which contains 10 ft * 4 ft * 1/6 ft = 6.66 cu. ft of gravel

So you will have roughly 815.81 cu. ft left when you're done!

Answer 4

Volume of a cone...
Is it bigger, equal to or less than the volume of a driveway 10ft x 4t x 2 inches deep... You will then have your answer.

Answer 5

I started to figure it for you but am curious about what you mean by a base of 5'... that throws me.

Answer 6

IDK the only thing I can tell you is that you need 80 square feet to fill the driveway. Sorry
: )