Math Help Forum: Inverted Cone

We want to use an inverted cone with a radius of 9cm to dispense 100mL of a chemical. To be certain that we dispense the correct quantity we want markings in 100mL increments on the outside of the cone. Where should we place the markings?(accurate to .1 of a mm).
The volume of the inverted cone can be found with V=(32a^3)/27 where a is the radius of the cone

So far all I have done is sub in the radius to work out the volume




Any help would be greatly appreciated

What exactly is the shape of the cone? That is, what is the total height when the radius is 9 cm? The volume of a cone, of radius a and height h, is . You say that the volume is given by which leads me to the conclusion that the height is . With a= 9 cm, that gives or about 0.318 cm. I find that hard to believe!

If a cone has radius R and height H, then for any given height, h, above the vertex, the radius at that height is given by or . A circle with that radius has area and, if we think of it as a thin disk of height dh, volume . We can find the volume between two different height, and by integrating that:
.

So the distance from , at the vertex, to the height, where the volume is 1000 ml is . Once you have solved for that h, set it equal to and solve for the next .

Unfortunately I had worked out the previous question that makes you find the function for the volume of the cone. Instead of it should actually be