Ask Me Help Desk - Writing a quadratic function for a cone

Quote:

Originally Posted by Smurfsnot2604

I was trying to make a function from the following word problem.

Grain is falling from a chute onto the ground forming a conical pile whose diameter is always three times it's height. How high will the be when there is 1700ft^3 of grain?

So basically I'm trying to make a function that will tell me the answer. I know it's a cone so Volume = (1/3) * radius^2 * (pi) * height. And the diameter = height * 3. So how would I put this together? I thought I knew but I had an option between 5 answers and didn't get any of them.

The choices were: 18.95, 15.04, 8.28, 8.97, and 5.65.

$V = \frac 13 \pi r^2 h$

$r = \frac 32 h$

combining the two we get:

$V = \frac 13 \pi \frac 94 h^3$

$1700\,ft^3 = \frac 34 \pi h^3$

$\frac {4 \times 1700\,ft^3}{3 \pi} \approx 721.5\,ft^3 =h^3$ take the cube root

$h \approx 8.97\,ft$

That's how I would do it.