# Calculate Volume of Bottle

#### chrisf8657

[h=1]How would you calculate the volume, or capacity, in mL of a bottle using only height and circumference in inches or mm? If you need to convert between something for mL, please show that.[/h]Mucho Thanks guys!

MHF Helper
1 mL = 1 cm^3

#### DenisB

A bottle? Depends on its shape, I guess.
Fill it with water, then empty it in a "measurable container".....???

#### HallsofIvy

MHF Helper
if your bottle is a cylinder, or can be reasonably approximated by a cylinder, then its volume is $$\displaystyle \pi r^2h$$ With r and h given in ml, the volume will be in cubic ml. There are 10 mm in a cm so 10(10)(10)= 1000 cubic mm in a cm so the volume, again if r and h are given in mm. then the volume is $$\displaystyle \frac{\pi r^2 h}{1000}$$ cubic cm. And, as skeeter said, one ml is exactly one cubic cm.

#### chrisf8657

Gentlemen,
Yes, its a perfect cylindrical bottle.

#### skeeter

MHF Helper
if your bottle is a cylinder, or can be reasonably approximated by a cylinder, then its volume is $$\displaystyle \pi r^2h$$ With r and h given in ml, the volume will be in cubic ml. There are 10 mm in a cm so 10(10)(10)= 1000 cubic mm in a cm so the volume, again if r and h are given in mm. then the volume is $$\displaystyle \frac{\pi r^2 h}{1000}$$ cubic cm. And, as skeeter said, one ml is exactly one cubic cm.
Halls really meant mm

MHF Helper
Yes, thank you.

#### chrisf8657

Trying to understand,

r = 33.17mm
h = 61.75mm
v = 213440.9 (assuming PI * (r ^ 2) * h)
result = 213.4409 (from 213440.9 / 1000)

The bottle is ~30mL, so this number is way off.
What am I doing wrong?

#### skeeter

MHF Helper
$r = 3.317 \, cm$

$h = 6.175 \, cm$

$V = \pi r^2 h = 213.4 \, cm^3 = 213.4 \, mL$

A cylinder with the dimensions you cite has the calculated volume above ... and you say the bottle has only 30 mL of volume?

If 30 mL is a "book" answer, then I disagree with it.

Did you make measurements on an actual "bottle"? Are you sure about your measurements? Given the number of significant figures in your measurements, did you use a set of calipers or some other very accurate device to make those measurements?

Is the bottle actually a cylinder? Maybe you should post a pic.

#### Archie

You are a factor of 10 out in your volume calculation! It should be $21cm^3$, plus change.