# Thread: Volume of cone with variable height

1. ## Volume of cone with variable height

I haven't really done much with volumes in the past, and this question is driving me insane.

A container is in the shape of an inverted cone of height 80cm and diameter 40 cm.

Find the volume, Vcm^3, of water in the container when the depth is x cm.

2. Originally Posted by freswood
I haven't really done much with volumes in the past, and this question is driving me insane.

A container is in the shape of an inverted cone of height 80cm and diameter 40 cm.

Find the volume, Vcm^3, of water in the container when the depth is x cm.

The volume of a cone is,
$V=\frac{1}{3}\pi r^2h$

When the depth is $x$ what is its radius at that time? Below is the picture of the section of the cone, note the similar triangles.
Thus,
$\frac{20}{r}=\frac{80}{x}$
Thus,
$r=x/4$
Thus,
$V=\frac{1}{3}\pi(x/4)^2x^2=\frac{1}{48}\pi x^3$

3. Thanks so much! Are you a mathematician, or just an enthusiast?

4. Originally Posted by freswood
Thanks so much! Are you amathematician
A mathematician is not a profession one may earn. As in, a scientist, physicist, engineer, doctor. Rather, it is a title given as a gift by humanity acknowledging his accomplishments which given him immortality.