duh -water capacity

[Deen]

Apologies if this appears twice but the first post isn't showing on my ng.

How do I work out the water capacity of a hexagonal tank 26 inches
wide(diameter across widest part) and 18 inches high? (In UK gallons)

[Deen]

"Dennis Fox" > wrote in message
...
> Deen wrote:
> > Apologies if this appears twice but the first post isn't showing on my
ng.
> >
> > How do I work out the water capacity of a hexagonal tank 26 inches
> > wide(diameter across widest part) and 18 inches high? (In UK gallons)
> >
> >
> >
>
>
> And I bet you thought that high school geometry course had no real-world
> applications you would ever need! ;-)
>
> Is the tank a true hexagon (all six vertical surfaces are the same
> size)? If so, then the hexagon can be divided into six equilateral
> triangles, with sides of 13 inches. So we can find the area of an
> equilateral triangle, take it times 6 to get the area of the hexagon;
> then times the height of the tank to get the volume.
>
> For an equilateral triangle:
> Area = 1/2 x base x height
> base = 13 inches
> height = 13 inches x sin(60 degrees) = 11.25 inches
>
> so for the triangle
> Area = 0.5 x 13 inches x 11.25 inches = 73.125 inches squared
>
> for the hexagon
> Area = 6 x 73.125 inches squared = 438.75 inches squared
>
> Volume of tank = Area of hexagon x height of tank
> volume = 438.75 inches squared x 18 inches = 7897.5 cubic inches
>
> Now to convert ... 1 cubic foot = 12" x 12" x 12" = 1728 cubic inches
> so your tank is 7897.5 cubic inches / 1728 cubic inches per cubic foot
> or approximately 4.57 cubic feet.
>
> Plugging that into Mike Edwardes' very handy Aquarium converter
> (http://mike-edwardes.members.beeb.net/converter.html) yields:
>
> 29.5 Imperial (UK) gallons or 35.5 US gallons.
>
> -Dennis

Wow! Thank you so much. I'd thought of dividing it into triangles but then
thought that there must be an easier way that my tired old brain had
forgotten. Obviously there isn't!.
Again thanks for the help
Denise

[Deen]

"Dennis Fox" > wrote in message
...
> Deen wrote:
> > Apologies if this appears twice but the first post isn't showing on my
ng.
> >
> > How do I work out the water capacity of a hexagonal tank 26 inches
> > wide(diameter across widest part) and 18 inches high? (In UK gallons)
> >
> >
> >
>
>
> And I bet you thought that high school geometry course had no real-world
> applications you would ever need! ;-)
>
> Is the tank a true hexagon (all six vertical surfaces are the same
> size)? If so, then the hexagon can be divided into six equilateral
> triangles, with sides of 13 inches. So we can find the area of an
> equilateral triangle, take it times 6 to get the area of the hexagon;
> then times the height of the tank to get the volume.
>
> For an equilateral triangle:
> Area = 1/2 x base x height
> base = 13 inches
> height = 13 inches x sin(60 degrees) = 11.25 inches
>
> so for the triangle
> Area = 0.5 x 13 inches x 11.25 inches = 73.125 inches squared
>
> for the hexagon
> Area = 6 x 73.125 inches squared = 438.75 inches squared
>
> Volume of tank = Area of hexagon x height of tank
> volume = 438.75 inches squared x 18 inches = 7897.5 cubic inches
>
> Now to convert ... 1 cubic foot = 12" x 12" x 12" = 1728 cubic inches
> so your tank is 7897.5 cubic inches / 1728 cubic inches per cubic foot
> or approximately 4.57 cubic feet.
>
> Plugging that into Mike Edwardes' very handy Aquarium converter
> (http://mike-edwardes.members.beeb.net/converter.html) yields:
>
> 29.5 Imperial (UK) gallons or 35.5 US gallons.
>
> -Dennis

Wow! Thank you so much. I'd thought of dividing it into triangles but then
thought that there must be an easier way that my tired old brain had
forgotten. Obviously there isn't!.
Again thanks for the help
Denise

[Deen]

"Dennis Fox" > wrote in message
...
> Deen wrote:
> > Apologies if this appears twice but the first post isn't showing on my
ng.
> >
> > How do I work out the water capacity of a hexagonal tank 26 inches
> > wide(diameter across widest part) and 18 inches high? (In UK gallons)
> >
> >
> >
>
>
> And I bet you thought that high school geometry course had no real-world
> applications you would ever need! ;-)
>
> Is the tank a true hexagon (all six vertical surfaces are the same
> size)? If so, then the hexagon can be divided into six equilateral
> triangles, with sides of 13 inches. So we can find the area of an
> equilateral triangle, take it times 6 to get the area of the hexagon;
> then times the height of the tank to get the volume.
>
> For an equilateral triangle:
> Area = 1/2 x base x height
> base = 13 inches
> height = 13 inches x sin(60 degrees) = 11.25 inches
>
> so for the triangle
> Area = 0.5 x 13 inches x 11.25 inches = 73.125 inches squared
>
> for the hexagon
> Area = 6 x 73.125 inches squared = 438.75 inches squared
>
> Volume of tank = Area of hexagon x height of tank
> volume = 438.75 inches squared x 18 inches = 7897.5 cubic inches
>
> Now to convert ... 1 cubic foot = 12" x 12" x 12" = 1728 cubic inches
> so your tank is 7897.5 cubic inches / 1728 cubic inches per cubic foot
> or approximately 4.57 cubic feet.
>
> Plugging that into Mike Edwardes' very handy Aquarium converter
> (http://mike-edwardes.members.beeb.net/converter.html) yields:
>
> 29.5 Imperial (UK) gallons or 35.5 US gallons.
>
> -Dennis

Wow! Thank you so much. I'd thought of dividing it into triangles but then
thought that there must be an easier way that my tired old brain had
forgotten. Obviously there isn't!.
Again thanks for the help
Denise

[Deen]

Now believe it or not I AM actually computer literate - it's just that my
mail server doesn't know this :-)). sorry folks - pc gremlins at work.